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Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Exponents Exercise 5A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the value of:
(i) 6²
(ii) 7³
(iii) 4⁴
(iv) 5⁵
(v) 8³
(vi) 7⁵
Solution:

Question 2.
Evaluate:
(i) 2³ x 4²
(ii) 2³ x 5²
(iii) 3³ x 5²
(iv) 2² x 3³
(v) 3² x 5²
(vi) 5³ x 2⁴
(vii) 3² x 4²
(ix) (5 x 4)²
Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Which is greater :
(i) 2³ or 3²
(ii) 2⁵ or 5²
(iii) 4³ or 3⁴
(iv) 5⁴ or 4⁵
Solution:

Question 6.
Express each of the following in exponential form :
(i) 512
(ii) 1250
(iii) 1458
(iv) 3600
(v) 1350
(vi) 1176
Solution:

Question 7.
If a = 2 and b = 3, find the value of:
(i) (a + b)²
(ii) (b – a)³
(iii) (a x b)^a
(iv) (a x b)^b
Solution:

Question 8.
Express:
(i) 1024 as a power of 2.
(ii) 343 as a power of 7.
(iii) 729 as a power of 3.
Solution:

Question 9.
If 27 x 32 = 3^x x 2^y; find the values of x and y.

Solution:

Question 10.
If 64 x 625 = 2^a x 5^b; find :
(i) the values of a and b.
(ii) 2^b x 5^a
Solution:

Exponents Exercise 5B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Fill in the blanks:
In 5² = 25, base = ……… and index = ……….
If index = 3x and base = 2y, the number = ………
Solution:

Question 2.
Evaluate:
(i) 2⁸ ÷ 2³
(ii) 2^3÷ 2⁸
(iii) (2⁶)⁰
(iv) (3^o)⁶
(v) 8³ x 8^-5 x 8⁴
(vi) 5⁴  x 5³ + 5⁵
(vii) 5⁴ ÷ 5³ x 5⁵
(viii) 4⁴ ÷ 4³ x 4⁰
(ix) (3⁵ x 4⁷ x 5⁸)⁰
Solution:

Question 3.
Simplify, giving Solutions with positive index:


Solution:

Question 4.
Simplify and express the Solution in the positive exponent form :


Solution:

Question 5.
Evaluate

Solution:

Question 6.
If m² = -2 and n = 2; find the values of:
(i) m + r² – 2mn
(ii) mⁿ + n^m
(iii) 6m^-3 + 4n²
(iv) 2n³ – 3m
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

Substitution Exercise 20A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the following blanks, when :
x = 3,y = 6, z = 18, a = 2, b = 8, c = 32 and d = 0.


Solution:

Question 2.
Find the value of :

Solution:

Question 3.
Find the value of :

Solution:

Question 4.
If a = 3, b = 0, c = 2 and d = 1, find the value of :

Solution:

Question 5.
Find the value of 5x² – 3x + 2, when x = 2.
Solution:

Question 6.
Find the value of 3x³ – 4x² + 5x – 6, when x = -1.
Solution:

Question 7.
Show that the value of x³ – 8x² + 12x – 5 is zero, when x = 1.
Solution:

Question 8.
State true and false :
(i) The value of x + 5 = 6, when x = 1
(ii) The value of 2x – 3 = 1, when x = 0
(iii) \(\frac { 2x-4 }{ x+1 }\) = -1,when x = 1
Solution:

Question 9.
If x = 2, y = 5 and z = 4, find the value of each of the following :

Solution:

Question 10.
If a = 3, find the values of a² and 2^a.
Solution:

Question 11.
If m = 2, find the difference between the values of 4m³ and 3m⁴.
Solution:

Substitution Exercise 20B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Evaluate :
(i) (23 – 15) + 4
(ii) 5x + (3x + 7x)
(iii) 6m – (4m – m)
(iv) (9a – 3a) + 4a
(v) 35b – (16b + 9b)
(vi) (3y + 8y) – 5y
Solution:

Question 2.
Simplify :


Solution:

Question 3.
Simplify :

Solution:

Substitution Exercise 20C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :

Solution:

Question 2.
Insert the bracket as indicated :

Solution:

Substitution Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the value of 3ab + 10bc – 2abc when a = 2, b = 5 and c = 8.
Solution:

Question 2.
If x = 2, y = 3 and z = 4, find the value of 3x² – 4y² + 2z².
Solution:

Question 3.
If x = 3, y = 2 and z = 1; find the value of:
(i) x^y
(ii) y^x
(iii) 3x² – 5y²
(iv) 2x – 3y + 4z + 5
(v) y² – x² + 6z²
(vi) xy + y²z – 4zx
Solution:

Question 4.
If P = -12x² – 10xy + 5y², Q = 7x² + 6xy + 2y², and R = 5x² + 2xy + 4y² ; find :
(i) P – Q
(ii) Q + P
(iii) P – Q + R
(iv) P + Q + R
Solution:

Question 5.
If x = a² – bc, y = b² – ca and z = c² – ab ; find the value of :
(i) ax + by + cz
(ii) ay – bx + cz
Solution:

Question 6.
Multiply and then evaluate :
(i) (4x + y) and (x – 2y); when x = 2 and y = 1.
(ii) (x² – y) and (xy – y²); when x = 1 and y = 2.
(iii) (x – 2y + z) and (x – 3z); when x = -2, y = -1 and z = 1.
Solution:

Question 7.
Simplify :
(i) 5 (x + 3y) – 2 (3x – 4y)
(ii) 3x – 8 (5x – 10)
(iii) 6 {3x – 8 (5x – 10)}
(iv) 3x – 6 {3x – 8 (5x – 10)}
(v) 2 (3x² – 4x – 8) – (3 – 5x – 2x²)
(vi) 8x – (3x – \(\bar { 2x-3 }\))
(vii) 12x² – (7x – \(\bar { 3x^{ 2 }+15 }\))
Solution:

Question 8.
If x = -3, find the value of : 2x³ + 8x² – 15.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

Fundamental Operations Exercise 19A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x²y + 18x²y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x²y + 3xy² = ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax² – 13a²x = ………….
Solution:

Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y = ………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:

Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Evaluate :

Solution:

Question 6.
Subtract the first term from the second :

Solution:

Question 7.
Simplify :


Solution:

Fundamental Operations Exercise 19B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the sum of :

Solution:

Question 2.
Add the following expressions :


Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Subtract :

Solution:

Question 5.

Solution:

Question 6.
From the sum of x + y – 2z and 2x – y + z subtract x + y + z.
Solution:

Question 7.
From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.
Solution:

Question 8.
Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.
Solution:

Question 9.
Subtract the sum of x + y and x – z from the sum of x – 2z and x + y + z
Solution:

Question 10.
By how much should x + 2y – 3z be increased to get 3x ?
Solution:

Question 11.
The sum of two expressions is 5x² – 3y². If one of them is 3x² + 4xy – y², find the other.
Solution:

Question 12.
The sum of two expressions is 3a² + 2ab – b². If one of them is 2a² + 3b², find the other.
Solution:

Fundamental Operations Exercise 19C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :

Solution:

Question 2.
Fill in the blanks :

Solution:

Question 3.
Find the value of :

Solution:

Question 4.
Multiply :


Solution:

Question 5.
Multiply :

Solution:

Question 6.
Multiply :

Solution:

Question 7.
Multiply :
(i) x + 2 and x + 10
(ii) x + 5 and x – 3
(iii) x – 5 and x + 3
(iv) x – 5 and x – 3
(v) 2x+ y and x+ 3y
(vi) (3x – 5y) and (x + 6y)
(vii) (x + 9y) and (x – 5y)
(viii) (2x + 5y) and (2x + 5y)
Solution:

Question 8.
Multiply :

Solution:

Question 9.
Find the product of :

Solution:

Fundamental Operations Exercise 19D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Divide :

Solution:

Question 2.
Simplify :


Solution:

Question 3.
Divide :


Solution:

Question 4.
Simplify :

Solution:

Question 5.
Divide :


Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 2 Exponents (Powers)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 2 Exponents (Powers)

Exponents Exercise 2A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
If 1125 = 3^m x 5ⁿ; find m and n.
Solution:

Question 3.
Find x, if 9 × 3^x = (27)^2x-3
Solution:

Exponents Exercise 2B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Compute:


Solution:

Question 2.
Simplify:
(i) \(8^{\frac{4}{3}}+25^{\frac{3}{2}}-\left(\frac{1}{27}\right)^{-\frac{2}{3}}\)
(ii) [(64)^-2]^-3 ÷ [{(-8)²}³]²
(iii) (2^-3 – 2^-4) (2^-3 + 2^-4)
Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Simplify:

Solution:

Question 5.
Simplify:
(x^a+b)^a-b.(x^b+c)^b-c.(x^c+a)^c-a
Solution:

Question 6.
Simplify:
(i) \(\sqrt[5]{x^{20} y^{-10} z^{5}}+\frac{x^{3}}{y^{3}}\)
(ii) \(\left(\frac{256 a^{16}}{81 b^{4}}\right)^{\frac{-3}{4}}\)
Solution:

Question 7.
(i) (a^-2)^-2. (ab)^-3
(ii) (xⁿy^-m)⁴ × (x³y^-2)^-n
(iii) \(\left(\frac{125 a^{-3}}{y^{6}}\right)^{\frac{-1}{3}}\)
(iv) \(\left(\frac{32 x^{-5}}{243 y^{-5}}\right)^{\frac{-1}{5}}\)
(v) (a^-2b)^1/2 × (ab^-3)^1/3
(vi) (xy)^m-n . (yz)^n-1 . (zx)^1-m
Solution:

Question 8.
Show that:

Solution:

Question 9.
Evaluate:

Solution:

Question 10.
Evaluate:

Solution:

Question 11.
(m + n)^-1 (m^-1 + n^-1) = (mn)^-1
Solution:

Question 12.
Prove that:

Solution:

Question 13.
Find the values of n, when:
(i) 12^-5 × 12²ⁿ⁺¹ = 12¹³ ÷ 12⁷
(ii) \(\frac{a^{2 n-3} \times\left(a^{2} \cdot\right)^{n+1}}{\left(a^{4}\right)^{-3}}\) = (a³)³ ÷ (a⁶)^-3
Solution:
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Question 14.
Simplify:

Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 4 Decimal Fractions (Decimals)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 4 Decimal Fractions (Decimals)

Decimal Fractions Exercise 4A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Convert the following into fractions in their lowest terms :
(i) 3.75
(ii) 0.5
(iii) 2.04
(iv) 0.65
(v) 2.405
(vi) 0.085
(vii) 8.025
Solution:

Question 2.
Convert into decimal fractions

Solution:

Question 3.
Write the number of decimal places in :
(i) 0.4762
(ii) 7.00349
(iii) 8235.403
(iv) 35.4
(v) 2.608
(vi) 0.000879
Solution:

Question 4.
Write the following decimals as word statements :
(i) 0.4,0.9,0.1
(ii) 1.9, 4.4, 7.5
(iii) 0.02, 0.56, 13.06
(iv) 0.005,0.207, 111.519
(v) 0.8, 0.08, 0.008, 0.0008
(vi)256.1, 10.22, 0.634
Solution:

Question 5.
Convert the given fractions into like fractions:
(i) 0.5,3.62,43.987 and 232.0037
(ii) 215.78, 33.0006, 530.3 and 0.03569
Solution:

Decimal Fractions Exercise 4B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Add:
(i) 0.5 and 0.37 (ii) 3.8 and 8.7
(iii) 0.02, 0.008 and 0.309
(iv) 0. 4136, 0. 3195 and 0.52
(v) 9.25, 3.4 and 6.666
(vi) 3.007, 0.587 and 18.341
(vii) 0.2, 0.02 and 2.0002
(viii) 6. 08, 60.8, 0.608 and 0.0608
(ix) 29.03, 0.0003, 0.3 and 7.2
(x) 3.4, 2.025, 9.36 and 3.6221
Solution:

Question 2.
Subtract the first! number from the second :
(i) 5.4, 9.8
(ii) 0.16, 4.3
(iii) 0.82, 8.6
(v) 2.237, 9.425
(vi) 41 .03, 59.46
(vii) 3.92. 26.86
(viii) 4.73, 8.5
(ix) 12.63, 36.2
(x) 0.845, 3.71
Solution:

Question 3.
Simplify :
(i) 28.796 -13.42 – 2.555
(ii) 93.354 – 62.82 – 13.045
(iii) 36 – 18.59 – 3.2
(iv) 86 + 16.95 – 3.0042
(v) 32.8 – 13 – 10.725 +3.517
(vi) 4000 – 30.51 – 753.101 – 69.43
(vii) 0.1835 + 163.2005 – 25.9 – 100
(viii) 38.00 – 30 + 200.200 – 0.230
(ix) 555.555 + 55.555 – 5.55 – 0.555
Solution:

Question 4.
Find the difference between 6.85 and 0.685.
Solution:

Question 5.
Take out the sum of 19.38 and 56.025 then subtract it from 200. 111.
Solution:

Question 6.
Add 13.95 and 1.003 ; and from the result, subtract the sum of 2.794 and 6.2.
Solution:

Question 7.
What should be added to 39.587 to give 80.375 ?
Solution:

Question 8.
What should be subtracted from 100 to give 19.29?
Solution:

Question 9.
What is the excess of 584.29 over 213.95 ?
Solution:

Question 10.
Evaluate:
(i) (5.4 – 0.8) + (2.97 -1.462)
(ii) (6.25 + 0.36) -(17.2 – 8.97)
(iii) 9.004 + (3 -2.462)
(iv) 879.4 – (87.94 – 8 .794)
Solution:

Question 11.
What is the excess of 75 over 48.29?
Solution:

Question 12.
If A = 237.98 and B = 83.47.
Find :
(i) A – B
(ii) B – A.
Solution:

Question 13.
The cost of one kg of sugar increases from ?28.47 to T32.65. Find the increase in cost.
Solution:

Decimal Fractions Exercise 4C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Multiply:
(i) 0.87 by 10
(ii) 2.948 by 100
(iii) 6.4 by 1000
(iv) 5.8 by 4
(v) 16.32 by 28
(vi) 5. 037 by 8
(vi) 4.6 by 2.1
(viii) 0.568 by 6.4
Solution:

Question 2.
Multiply each number by 10, 100, 1000 :
(i) 0.5
(ii) 0.112
(iii) 4.8
(iv) 0.0359
(v) 16.27
(vi) 234.8
Solution:

Question 3.
Evaluate:
(i) 5.897 x 2.3
(ii) 0.894 x 87
(iii) 0.01 x 0.001
(iv) 0.84 x 2.2 x 4
(v) 4.75 x 0.08 x 3
(vi) 2.4 x 3.5 x 4.8
(vii) 0.8 x 1.2 x 0.25
(viii) 0.3 x 0.03 x 0.003
(ix) 12.003 x (0.2)⁵
Solution:

Question 4.
Divide :
(i) 54.9 by 10
(ii) 7.8 by 100
(iii) 324.76 by 1000
(iv) 12.8 by 4
(v) 27.918 by 9
(vi) 4.672 by 8
(vii) 4.32 by 1.2
(viii) 7.644 by 1.4
(ix) 4.8432 by 0.08
Solution:

Question 5.
Divide each of the given numbers by 10, 100, 1000 and 10000
(i) 2.1
(ii) 8.64
(iii) 5-01
(iv) 0.0906
(v) 0.125
(vi) 111.11
(vii) 0.848 x 3
(viii)4.906 x (0.2) ²
(ix) (1.2)² x(0.9)²
Solution:

Question 6.
Evaluate :
(i) 9.75 + 5
(ii) 4.4064 + 4
(iii) 27.69 + 30
(iv) 19.25 + 25
(v) 20.64+ 16
(vi) 3.204 + 9
(vii) 0.125 + 25
(viii) 0.14616 + 72
(ix) 0.6227+ 1300
(x) 257.894+ 0-169
(xi) 6.3 + (0.3)²
Solution:

Question 7.
Evaluate:
(i) 4.3 x 0.52 x 0.3
(ii) 3.2 x 2.5 x 0.7
(iii) 0.8 x 1.5 x 0.6
(iv) 0.3 x 0.3 x 0.3
(v) 1.2 x 1.2 x 0.4
(vi) 0.4 x 0.04 x 0.004
(vii) 0.5 x 0.6 x 0.7
(Viii) 0.5 x 0.06 x 0.007
Solution:

Question 8.
Evaluate:
(i) (0.9)²
(ii) (0.6)² x 0.5
(iii) 0.3 x (0.5)²
(iv) (0.4)³
(v) (0.2)³ x 5
(vi) (0.2)³ x 0.05
Solution:

 Question 9.
Find the cost of 36.75 kg wheat at the rate of ₹12.80 per kg.
Solution:

Question 10.
The cost of a pen is ₹56.15. Find the cost of 16 such pens.
Solution:

Question 11.
Evaluate:
(i) 0.0072 ÷ 0.06
(ii) 0.621 ÷ 0.3
(iii) 0.0532 ÷ 0.005
(iv) 0.01162 ÷ 0.14
(v) (7.5 x 40.4) ÷ 25
(vi) 2.1 ÷ (0.1 x 0.1)
Solution:

Question 12.
Fifteen indentical articles weigh 31.50 kg. Find the weight of each article.
Solution:

Question 13.
The product of two numbers is 211.2. If one of these two numbers is 16.5, find the other number.
Solution:

Question 14.
One dozen identical articles cost ₹45.96. Find the cost of each article.
Solution:

Decimal Fractions Exercise 4D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find whether the given division forms a terminating decimal or a non-terminating decimal:
(i) 3 ÷ 8
(ii) 8 ÷ 3
(iii) 6÷ 5
(iv) 5 ÷ 6
(v) 12.5 ÷ 4
(vi) 23 ÷ 0.7
(vii) 42 ÷ 9
(viii) 0.56÷ 0.11
Solution:

Question 2.
Express as recurring decimals :

Solution:

Question 3.
Convert into vulgar fraction :
(i) 0.\(\bar { 3 }\)
(ii) 0.\(\bar { 8 }\)
(iii) 4.\(\bar { 4 }\)
(iv) 23.\(\bar { 7 }\)
Solution:

Question 4.
Convert into vulgar fraction :
(i) 0.\(\bar { 35 }\)
(ii) 2.\(\bar { 23 }\)
(iii) 1.\(\bar { 28 }\)
(iv) 5.\(\bar { 234 }\)
Solution:

Question 5.
Convert into vulgar fraction :
(i) 0 0.3\(\bar { 7 }\)
(ii) 0.2\(\bar { 45 }\)
(iii) 0.68\(\bar { 5 }\)
(iv) 0.4\(\bar { 42 }\)
Solution:

Decimal Fractions Exercise 4E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Round off:
(i) 0 .07, 0.112, 3.59, 9.489 to the nearest tenths.
(ii) 0.627, 100.479, 0 065 and 0.024 to the nearest hundredths.
(iii) 4.83,0.86,451 .943 and 9.08 to the nearest whole number.
Solution:

Question 2.
Simplify, and write your answers correct to the nearest hundredths :
(i) 18 .35 x 1.2
(ii) 62.89 x 0.02
Solution:

Question 3.
Write the number of significant figures (digits) in:
(i) 35.06
(ii) 0.35
(iii) 7.0068
(iv) 19 .0
(v) 0.0062
(vi) 0 4.2 x 0.6
(vii) 0.08 x 25
(viii) 3.6 ÷ 0.12 .
Solution:

Question 4.
Write :
(i) 35.869,0 008426,4.952 and 382.7, correct lo three significant figures.
(ii) 60.974. 2.8753, 0.001789 and 400.04, correct to four significant figures.
(iii) 14.29462, 19.2, 46356.82 and 69, correct to five significant figures.
Solution:

Decimal Fractions Exercise 4F – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The weight of an object is 3 .06 kg. Find the total weight of 48 similar objects.
Solution:

Question 2.
Find die cost of 17.5 m cloth at the rate of Rs. 112.50 per metre.
Solution:

Question 3.
One kilogramme of oil costs Rs. 73.40. Find the cost of 9.75 kilogramme of the oil.
Solution:

Question 4.
Total weight of 8 identical objects is 51.2 kg. Find the weight of each object.
Solution:

Question 5.
18.5 m of cloth costs Rs. 666. Find the cost of 3.8 m cloth.
Solution:

Question 6.
Find die value of:
(i) 0.5 of Rs. 7.60 + 1.62 of Rs. 30
(ii) 2.3 of 7.3 kg + 0.9 of 0.48 kg
(iii) 6.25 of 8.4 – 4.7 of 3.24
(iv) 0.98 of 235 – 0 .09 of 3.2
Solution:

Question 7.
Evaluate:
(i) 5.6 – 1 .5 of 3.4
(ii) 4.8 ÷ 0.04 of 5
(iii) 0.72 of 80 + 0.2
(iv) 0.72 ÷ 80 of 0.2
(v) 6.45 + (3.9 – 1.75)
(vi) 0.12 of(0.104 – 0.02)+ 0.36 x 0.5
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 1 Rational Numbers

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 1 Rational Numbers

Rational Numbers Exercise 1A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Add, each pair of rational numbers, given below, and show that their addition (sum) is also a rational number:

Solution:

Question 2.
Evaluate:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
For each pair of rational numbers, verify commutative property of addition of rational numbers:

Solution:

Question 5.
For each set of rational numbers, given below, verify the associative property of addition of rational numbers:

Solution:

Question 6.
Write the additive inverse (negative) of:

Solution:

Question 7.
Fill in the blanks:

Solution:

Question 8.
State, true or false:

Solution:

Rational Numbers Exercise 1B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Subtract:

Solution:

Question 3.
The sum of two rational numbers is \(\frac { 9 }{ 20 }\). If one of them is \(\frac { 2 }{ 5 }\), find the other.
Solution:

Question 4.
The sum of the two rational numbers is \(\frac { -2 }{ 3 }\). If one of them is \(\frac { -8 }{ 5 }\), find the other.
Solution:

Question 5.
The sum of the two rational numbers is -6. If one of them is \(\frac { -8 }{ 5 }\), find the other.
Solution:

Question 6.
Which rational number should be added to \(\frac { -7 }{ 8 }\) to get \(\frac { 5 }{ 9 }\) ?
Solution:

Question 7.
Which rational number should be added to \(\frac { -5 }{ 9 }\) to get \(\frac { -2 }{ 3 }\) ?
Solution:

Question 8.
Which rational number should be subtracted from \(\frac { -5 }{ 6 }\) to get \(\frac { 4 }{ 9 }\) ?
Solution:

Question 9.
(i) What should be subtracted from -2 to get \(\frac { 3 }{ 8 }\)
(ii) What should be added to -2 to get \(\frac { 3 }{ 8 }\)
Solution:

Question 10.
Evaluate:

Solution:

Rational Numbers Exercise 1C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Multiply:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Multiply each rational number, given below, by one (1):

Solution:

Question 5.
For each pair of rational numbers, given below, verify that the multiplication is commutative:

Solution:

Question 6.
Write the reciprocal (multiplicative inverse) of each rational number, given below :

Solution:

Question 7.
Find the reciprocal (multiplicative inverse) of:

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Name the multiplication property of rational numbers shown below :

Solution:

Question 11.
Fill in the blanks:
(i) The product of two positive rational numbers is always ……………
(ii) The product of two negative rational numbers is always ……………
(iii) If two rational numbers have opposite signs then their product is always …………..
(iv) The reciprocal of a positive rational number is ………. and the reciprocal of a negative rational number is ……………
(v) Rational number 0 has ………….. reciprocal.
(vi) The product of a rational number and its reciprocal is ………..
(vii) The numbers ……….. and ……….. are their own reciprocals.
(viii) If m is reciprocal of n, then the reciprocal of n is ………….
Solution:

Rational Numbers Exercise 1D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Divide:

Solution:

Question 3.
The product of two rational numbers is -2. If one of them is \(\frac { 4 }{ 7 }\), find the other.
Solution:

Question 4.
The product of two numbers is \(\frac { -4 }{ 9 }\). If one of them is \(\frac { -2 }{ 27 }\), find the other.
Solution:

Question 5.
m and n are two rational numbers such that

Solution:

Question 6.
By what number must \(\frac { -3 }{ 4 }\) be multiplied so that the product is \(\frac { -9 }{ 16 }\) ?
Solution:

Question 7.
By what number should \(\frac { -8 }{ 13 }\) be multiplied to get 16?
Solution:

Question 8.
If 3\(\frac { 1 }{ 2 }\) litres of milk costs ₹49, find the cost of one litre of milk?
Solution:

Question 9.
Cost of 3\(\frac { 2 }{ 5 }\) metre of cloth is ₹88\(\frac { 1 }{ 2 }\). What is the cost of 1 metre of cloth?
Solution:

Question 10.
Divide the sum of \(\frac { 3 }{ 7 }\) and \(\frac { -5 }{ 14 }\) by \(\frac { -1 }{ 2 }\).
Solution:

Question 11.

Solution:

Question 12.
The product of two rational numbers is -5. If one of these numbers is \(\frac { -7 }{ 15 }\), find the other.
Solution:

Question 13.
Divide the sum of \(\frac{5}{8}\) and \(\frac{-11}{12}\) by the difference of \(\frac{3}{7}\) and \(\frac{5}{14}\)
Solution:

Rational Numbers Exercise 1E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.
Insert one rational number between (0 7 and 8 (ii) 3.5 and 5
(i) 2 and 3.2
(ii) 3.5 and 5
(iii) 2 and 3.2
(iv) 4.2 and 3.6
(v) \(\frac { 1 }{ 2 }\) and 2
Solution:

Question 4.
Insert two rational numbers between
(i) 6 and 7
(ii) 4.8 and 6
(iii) 2.7 and 6.3
Solution:

Question 5.
Insert three rational numbers between
(i) 3 and 4
(ii) 10 and 12
Solution:

Question 6.
Insert five rational numbers between \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\)
Solution:

Question 7.
Insert six rational numbers between \(\frac { 5 }{ 6 }\) and \(\frac { 8 }{ 9 }\)
Solution:

Question 8.
Insert seven rational numbers between 2 and 3.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Fundamental Concepts Exercise 18A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 8 and x is equal to y.
(ii) x decreased by 5 is equal to y.
(iii) The sum of 2 and x is greater than y.
(iv) The sum of x and y is less than 24.
(v) 15 multiplied by m gives 3n.
(vi) Product of 8 and y is equal to 3x.
(vii) 30 divided by b is equal to p.
(viii) z decreased by 3x is equal to y.
(ix) 12 times of x is equal to 5z.
(x) 12 times of x is greater than 5z.
(xi) 12 times of x is less than 5z.
(xii) 3z subtracted from 45 is equal to y.
(xiii) 8x divided by y is equal to 2z.
(xiv) 7y subtracted from 5x gives 8z.
(xv) 7y decreased by 5x gives 8z.
Solution:

Question 2.
For each of the following algebraic expressions, write a suitable statement in words:
(i) 3x + 8=15
(ii) 7 – y > x
(iii) 2y – x < 12
(iv) 5 ÷ z = 5
(v) a + 2b > 18
(vi) 2x – 3y= 16
(vii) 3a – 4b > 14
(viii) b + 7a < 21
(ix) (16 + 2a) – x > 25
(x) (3x + 12) – y < 3a
Solution:

Fundamental Concepts Exercise 18B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Separate the constants and the variables from each of the following:

Solution:

Question 2.
Group the like terms together :

Solution:

Question 3.
State whether true or false :
(i) 16 is a constant and y is a variable but 16y is variable.
(ii) 5x has two terms 5 and x.
(iii) The expression 5 + x has two terms 5 and x
(iv) The expression 2x² + x is a trinomial.
(v) ax² + bx + c is a trinomial.
(vi) 8 x ab is a binomial.
(vii) 8 + ab is a binomial.
(viii) x³ – 5xy + 6x + 7 is a polynomial.
(ix) x³ – 5xy + 6x + 7 is a multinomial.
(x) The coefficient of x in 5x is 5x.
(xi) The coefficient of ab in – ab is – 1.
(xii) The coefficient of y in – 3xy is – 3
Solution:

Question 4.
State the number of terms in each of the following expressions :

Solution:

Question 5.
State whether true or false:
(i) xy and – yx are like terms.
(ii) x²y and – y²x are like terms.
(iii) a and – a are like terms.
(iv) – ba and 2ab are unlike terms.
(v) 5 and 5x are like terms.
(vi) 3xy and 4xyz are unlike terms.
Solution:

Question 6.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

Solution:

Question 7.
Write down the coefficient of x in the following monomial :

Solution:

Question 8.
Write the coefficient of :

Solution:

Question 9.
State the numeral coefficient of the following monomials :

(vii) – 7x ÷ y
(viii) – 3x ÷ (2y)
Solution:

Question 10.
Write the degree of each of the following polynomials :

Solution:

Fundamental Concepts Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 3x and 4y is 8.
(ii) 5x decreased by 7 gives y.
(iii) 31 added to 4x gives 6x.
(iv) 3x subtracted from 89 gives 44.
Solution:

Question 2.
Group the like terms :

Solution:

Question 3.
Write the number of terms in each of the following polynomials :

Solution:

Question 4.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:
(i) x + y
(ii) 5x – 4y
(iii) 7x² + 5x + 8
(iv) 64 + 3 ÷ 6
(v) 9 ÷ a x b
(vi) 8a ÷ b
Solution:

Question 5.
Write the coefficient of x2y in :
(i) -7x²yz
(ii) 8abx²y
(iii) – x²y
Solution:

Question 6.
Write the coefficient of :
(i) x² in – 8x²y
(ii) y in -4y
(iii) x in – xy²
Solution:

Question 7.
Write the numeral coefficient in :

Solution:

Question 8.
Write the degree of each of the following polynomials :

Solution:

Question 9.
Write each statement, given below in algebraic form :
(i) 28 more than twice of x is equal to 45.
(ii) 3y reduced by 5z is greater than 8x.
(iii) 6x divided by 13y is less than 17.
(iv) 9 multiplied by 5x is equal to 2y.
Solution:

Question 10.
State whether true or false :
(i) If 23 is a constant and x is a variable, 23 + x is constant.
(ii) If 23 is a constant and x is a variable, 23x is a variable.
(iii) If y is a variable and 57 is a constant, y – 57 is a variable.
(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)

Fundamental Concepts Exercise 11A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Separate constant terms and variable terms from tile following :

Solution:

Question 2.
Constant is only 8 others are variables
(i) 2x ÷ 15
(ii) ax+ 9
(iii) 3x² × 5x
(iv) 5 + 2a-3b
(v) 2y – \(\frac { 7 }{ 3 }\) z÷x
(vi) 3p x q ÷ z
(vii) 12z ÷ 5x + 4
(viii) 12 – 5z – 4
(ix) a³ – 3ab² x c
Solution:

Question 3.
Write the coefficient of:
(i) xy in – 3axy
(ii) z² in p²yz²
(iii) mn in -mn
(iv) 15 in – 15p²
Solution:

Question 4.
For each of the following monomials, write its degree :
(i) 7y
(ii) – x²y
(iii) xy²z
(iv) – 9y²z³
(v) 3 m³n⁴
(vi) – 2p²q³r⁴
Solution:

Question 5.
Write the degree of each of the following polynomials :
(i) 3y³-x²y² + 4x
(ii) p³q² – 6p²q⁵ + p⁴q⁴
(iii) – 8mn⁶+ 5m³n
(iv) 7 – 3x²y + y²
(v) 3x – 15
(vi) 2y²z + 9yz³
Solution:

Question 6.
Group the like term together :
(i) 9x², xy, – 3x², x² and – 2xy
(ii) ab, – a²b, – 3ab, 5a²b and – 8a²b
(iii) 7p, 8pq, – 5pq – 2p and 3p
Solution:

Question 7.
Write numerical co-efficient of each of the followings :
(i) y
(ii) -y
(iii) 2x²y
(iv) – 8xy³
(v) 3py²
(vi) – 9a²b³
Solution:

Question 8.
In -5x³y²z⁴; write the coefficient of:
(i) z²
(ii) y²
(iii) yz²
(iv) x³y
(v) -xy²
(vi) -5xy²z
Also, write the degree of the given algebraic expression.
Solution:

EXERCISE 11 (B)

Question 1.
Fill in the blanks :
(i) 8x + 5x = ………
(ii) 8x – 5x =……..
(iii) 6xy² + 9xy² =……..
(iv) 6xy² – 9xy² = ………
(v) The sum of 8a, 6a and 5b = ……..
(vi) The addition of 5, 7xy, 6 and 3xy = …………
(vii) 4a + 3b – 7a + 4b = ……….
(viii) – 15x + 13x + 8 = ………
(ix) 6x²y + 13xy² – 4x²y + 2xy² = ……..
(x) 16x² – 9x² = and 25xy² – 17xy²=………

Solution :

Question 2.
Add :
(i)- 9x, 3x and 4x
(ii) 23y², 8y² and – 12y²
(iii) 18pq – 15pq and 3pq

Solution:

Question 3.
Simplify :
(i) 3m + 12m – 5m
(ii) 7n² – 9n² + 3n²
(iii) 25zy—8zy—6zy
(iv) -5ax² + 7ax² – 12ax²
(v) – 16am + 4mx + 4am – 15mx + 5am
Solution:

Question 4.
Add :
(i) a + b and 2a + 3b
(ii) 2x + y and 3x – 4y
(iii)- 3a + 2b and 3a + b
(iv) 4 + x, 5 – 2x and 6x
Solution:

Question 5.
Find the sum of:
(i) 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z
(ii) 3a + 5b + 2c, 2a + 3b-c and a + b + c.
(iii) 4x²+ 8xy – 2y² and 8xy – 5y² + x²
(iv) 9x² – 6x + 7, 5 – 4x and 6 – 3x²
(v) 5x² – 2xy + 3y² and – 2x² + 5xy + 9y²
and 3x² -xy- 4y²
(vi) a² + b² + 2ab, 2b² + c² + 2bc
and 4c²-a² + 2ac
(vii) 9ax – 6bx + 8, 4ax + 8bx – 7
and – 6ax – 46x – 3
(viii) abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca
and 2ab – 3abc – 6ac
(ix) 4a² + 5b² – 6ab, 3ab, 6a² – 2b²
and 4b² – 5 ab
(x) x² + x – 2, 2x – 3x² + 5 and 2x² – 5x + 7
(xi) 4x³ + 2x² – x + 1, 2x³ – 5x²– 3x + 6, x² + 8 and 5x³ – 7x
Solution:

Question 6.
Find the sum of:
(i) x and 3y
(ii) -2a and +5
(iii) – 4x² and +7x
(iv) +4a and -7b
(v) x³+3x²y and 2y²
(vi) 11 and -by
Solution:

Question 7.
The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.
Solution:

Question 8.
The two adjacent sides of a rectangle are 6a + 96 and 8a – 46. Find its, perimeter.
Solution

Question 9.
Subtract the second expression from the first:

Solution:

Question 10.
Subtract:

Solution:

Question 11.
Subtract – 5a² – 3a + 1 from the sum of 4a² + 3 – 8a and 9a – 7.
Solution:

Question 12.
By how much does 8x³ – 6x² + 9x – 10 exceed 4x³ + 2x² + 7x -3 ?
Solution:

Question 13.
What must be added to 2a³ + 5a – a² – 6 to get a² – a – a³ + 1 ?
Solution:

Question 14.
What must be subtracted from a² + b² + lab to get – 4ab + 2b² ?
Solution:

Question 15.
Find the excess of 4m² + 4n² + 4p² over m²+ 3n² – 5p²
Solution:

Question 16.
By how much is 3x³ – 2x²y + xy² -y³ less than 4x³ – 3x²y – 7xy² +2y³
Solution:

Question 17.
Subtract the sum of 3a² – 2a + 5 and a² – 5a – 7 from the sum of 5a² -9a + 3 and 2a – a² – 1
Solution:

Question 18.
The perimeter of a rectangle is 28x³+ 16x² + 8x + 4. One of its sides is 8x² + 4x. Find the other side
Solution:

Question 19.
The perimeter of a triangle is 14a² + 20a + 13. Two of its sides are 3a² + 5a + 1 and a² + 10a – 6. Find its third side.
Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.
Simplify:

Solution:

EXERCISE 11 (C)

Question 1.
Multiply:

Solution:

Question 2.
Copy and complete the following multi-plications :

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Evaluate:

Solution:

Question 5.
Evaluate :

Solution:

Question 6.
Multiply:

Solution:

Question 7.
Multiply:

Solution:

EXERCISE 11 (D)

Question 1.
Divide:

Solution:

Question 2.
Divide :

Solution:

Question 3.
The area of a rectangle is 6x²– 4xy – 10y² square unit and its length is 2x + 2y unit. Find its breadth
Solution:

Question 4.
The area of a rectangular field is 25x² + 20xy + 3y² square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.
Solution:

Question 5.
Divide:

Solution:

EXERCISE 11 (E)

Simplify
Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Question 26.

Solution:

EXERCISE 11 (F)

Enclose the given terms in brackets as required :

Question 1.
 x – y – z = x-{…….)
Solution:

Question 2.
x² – xy² – 2xy – y² = x² – (…….. )
Solution:

Question 3.
4a – 9 + 2b – 6 = 4a – (…….. )
Solution:

Question 4.
x² -y² + z² + 3x – 2y = x² – (…….. )
Solution:

Question 5.
– 2a² + 4ab – 6a²b² + 8ab² = – 2a (……… )
Solution:

Simplify :

Question 6.
2x – (x + 2y- z)
Solution:

Question 7.
p + q – (p – q) + (2p – 3q)
Solution:

Question 8.
9x – (-4x + 5)
Solution:

Question 9.
6a – (- 5a – 8b) + (3a + b)
Solution:

 Question 10.
(p – 2q) – (3q – r)
Solution:

Question 11.
9a (2b – 3a + 7c)
Solution:

Question 12.
-5m (-2m + 3n – 7p)
Solution:

Question 13.
-2x (x + y) + x²
Solution:

Question 14.

Solution:

Question 15.
8 (2a + 3b – c) – 10 (a + 2b + 3c)
Solution:

Question 16.

Solution:

Question 17.
5 x (2x + 3y) – 2x (x – 9y)
Solution:

Question 18.
a + (b + c – d)
Solution:

Question 19.
5 – 8x – 6 – x
Solution:

Question 20.
2a + (6- \(\overline { a-b }\) )
Solution:

Question 21.
3x + [4x – (6x – 3)]
Solution:

Question 22.
5b – {6a + (8 – b – a)}
Solution:

Question 23.
2x-[5y- (3x -y) + x]
Solution:

Question 24.
6a – 3 (a + b – 2)
Solution:

Question 25.
8 [m + 2n-p – 7 (2m -n + 3p)]
Solution:

Question 26.
{9 – (4p – 6q)} – {3q – (5p – 10)}
Solution:

Question 27.
2 [a – 3 {a + 5 {a – 2) + 7}]
Solution:

Question 28.
5a – [6a – {9a – (10a – \(\overline { 4a-3a }\)  )}]
Solution:

Question 29.
9x + 5 – [4x – {3x – 2 (4x – 3)}]
Solution:

Question 30.
(x + y – z)x + (z + x – y)y – (x + y – z)z
Solution:

Question 31.
-1 [a-3 {b -4 (a-b-8) + 4a} + 10]
Solution:

Question 32.

Solution:

Question 33.
10 – {4a – (7 – \(\overline { a-5 }\)) – (5a – \(\overline { 1+a }\))}
Solution:

Question 34.
7a- [8a- (11a-(12a- \(\overline { 6a-5a }\))}]
Solution:

Question 35.

Solution:

Question 36.
x-(3y- \(\overline { 4z-3x }\) +2z- \(\overline { 5y-7x }\))
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Idea of Speed, Distance and Time Exercise 17A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?
Solution:

Question 2.
A motorist travelled the distance between two towns, which is 65 km, in 2 hours and 10 minutes. Find his speed in metre per minute.
Solution:

Question 3.
A train travels 700 metres in 35 seconds. What is its speed in km/h?
Solution:

Question 4.
A racing car covered 600 km in 3 hours 20 minutes. Find its speed in metre per second. How much distance will the car cover in 50 sec?
Solution:

Question 5.
Rohit goes 350 km in 5 hours. Find :
(i) his speed
(ii) the distance covered by Rohit in 6.2 hours
(iii) the time taken by him to cover 210 km.
Solution:

Question 6.
A boy drives his scooter with a uniform speed of 45 km/h. Find :
(i) the distance covered by him in 1 hour 20 min.
(ii) the time taken by him to cover 108 km.
(iii) the time taken to cover 900 m.
Solution:

Question 7.
I travel a distance of 10 km and come back in 2\(\frac { 1 }{ 2 }\) hours. What is my speed?
Solution:

Question 8.
A man walks a distance of 5 km in 2 hours. Then he goes in a bus to a nearby town, which is 40 km, in further 2 hours. From there, he goes to his office in an autorickshaw, a distance of 5 km, in \(\frac { 1 }{ 2 }\) hour. What was his average speed during the whole journey?
Solution:

Question 9.
Jagan went to another town such that he covered 240 km by a car going at 60 kmh^-1. Then he covered 80 km by a train, going at 100 kmh^-1 and the rest 200 km, he covered by a bus, going at 50 kmh^-1. What was his average speed during the whole journey?
Solution:

Question 10.
The speed of sound in air is about 330 ms^-1. Express this speed in kmh^-1. How long will the sound take to travel 99 km?
Solution:

Idea of Speed, Distance and Time Exercise 17B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train 180 m long is running at a speed of 90 km/h. How long will it take to pass a railway signal?
Solution:

Question 2.
A train whose length is 150 m, passes a telegraph pole in 10 sec. Find the speed of the train in km/h.
Solution:

Question 3.
A train 120 m long passes a railway platform 160 m long in 14 sec. How long will it take to pass another platform which is 100 m long?
Solution:

Question 4.
Mr. Amit can walk 8 km in 1 hour 20 minutes.
(a) How far does he go in :
(i) 10 minutes?
(ii) 30 seconds?
(b) How long will it take him to walk :
(i) 2500 m?
(ii) 6.5 km?
Solution:

Question 5.
Which is greater : a speed of 45 km/h or a speed of 12.25 m/sec?
How much is the distance travelled by each in 2 seconds?
Solution:

Question 6.
A and B start from the same point and at the same time with speeds 15 km/h and 12 km/h respectively, find the distance between A and B after 6 hours if both move in :
(i) same direction
(ii) the opposite directions.
Solution:

Question 7.
A and B start from the same place, in the same direction and at the same time with speeds 6 km/h and 2 m/sec respectively. After 5 hours who will be ahead and by how much?
Solution:

Question 8.
Mohit covers a certain distance in 6 hrs by his scooter at a speed of 40 kmh^-1.
(i) Find the time taken by Manjoor to cover the same distance by his car at the speed of 60 kmh^-1.
(ii) Find the speed of Joseph, if he takes 8 hrs to complete the same distance.
Solution:

Question 9.
A boy swims 200 m in still water and then returns back to the point of start in total 10 minutes. Find the speed of his swim in
(i) ms^-1
(ii) kmh^-1.
Solution:

Question 10.
A distance of 14.4 km is covered in 2 horus 40 minutes. Find the speed in ms^-1. With this speed Sakshi goes to her school, 240 m away from her house and then returns back. How much time, in all, will Sakshi take?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Percent Exercise 16A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in the percentage form :
(i) 13 out of 20
(ii) 21 eggs out of 30 are good
Solution:

Question 2.
Express the following fractions as percent :

Solution:

Question 3.
Express as percent:
(i) 0.10
(ii) 0.02
(iii) 0.7
(iv) 0.15
(v) 0.032
Solution:

Question 4.
Convert into fractions in their lowest terms:
(i) 8%
(ii) 20%
(iii) 85%
(iv) 250%
(v) 12\(\frac { 1 }{ 2 }\) %
Solution:

Question 5.
Express as decimal fractions :
(i) 25%
(ii) 108%
(iii) 95%
(iv) 4.5%
(v) 29.2%
Solution:

Question 6.
Express each of the following natural numbers as percent :
(i) 7
(ii) 2
(iii) 19.5
(iv) 5.37
Solution:

Percent Exercise 16B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express :
(i) Rs 5 as a percentage of Rs 25.
(ii) 80 paise as a percent of Rs 4.
(iii) 700 gm as a percentage of 2.8 kg.
(iv) 90 cm as a percent of 4.5 m.
Solution:

Question 2.
Express the first quantity as a percent of the second :
(i)) 40 P, ₹ 2
(ii) 500 gm, 6 kg
(iii) 42 seconds, 6 minutes
Solution:

Question 3.
Find the value of each of the following:
(i) 20% of ₹ 150
(ii) 90% of 130
(iii) 15% of 2 minutes
(iv) 7.5 % of 500 kg.
Solution:

Question 4.
If a man spends 70% of his income, what percent does he save ?
Solution:

Question 5.
A girl gets 65 marks out of 80. What percent marks did she get?
Solution:

Question 6.
A class contains 25 children, of which 6 are girls. What percentage of the class are the boys.
Solution:

Question 7.
A tin contains 20 litres of petrol. Due to leakage, 3 litres of petrol is lost. What percent is still present in the tin?
Solution:

Question 8.
An alloy of copper and zinc contains 45% copper and the rest is zinc. Find the weight of zinc in 20 kg of the alloy.
Solution:

Question 9.
A boy got 60 out of 80 in Hindi, 75 out of 100 in English and 65 out of 70 in Arithmetic. In which subject his percentage of marks the best ? Also, find his overall percentage.
Solution:

Question 10.
In a camp, there were 500 soldiers. 60 more soldiers joined them. What percent of the earlier (original) number have joined the camp.
Solution:

Question 11.
In a plot of ground of area 6000 sq. m, only 4500 sq. m is allowed for construction. What percent is to be left without construction?
Solution:

Question 12.
Mr. Sharma has a monthly salary of ₹ 8,000. If he spends ₹ 6,400 every month; find :
(i) his monthly expenditure as percent.
(ii) his monthly savings as percent.
Solution:

Question 13.
The monthly salary of Rohit is ₹ 24,000. If his salary increases by 12%, find his new monthly salary
Solution:

Question 14.
In a sale, the price of an article is reduced by 30%. If the original price of the article is ₹ 1,800, find :
(i) the reduction in the price of the article
(ii) reduced price of the article.
Solution:

Question 15.
Evaluate :
(i) 30% of 200 + 20% of 450 – 25% of 600
(ii) 10% of ₹ 450 – 12% of ₹ 500 + 8% of ₹ 500.
Solution:

Percent Exercise 16C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The price of rice rises from Rs. 30 per kg to Rs. 36 per kg. Find the percentage rise in the price of rice.
Solution:

Question 2.
The population of a small locality was 4000 in 1979 and 4500 in 1981, By what percent had the population increase ?
Solution:

Question 3.
The price of a scooter was ₹ 8000 in 1975. It came down to ₹ 6000 in 1980. By what percent had the price of the scooter came down?
Solution:

Question 4.
Find the resulting quantity when :
(i) ₹ 400 is decreased by 8%.
(ii) 25 km is increased by 5%.
(iii) a speed of 600 km/h is increased by 12\(\frac { 1 }{ 2 }\) %
(iv) there is 2.5% increase in a salary of ₹ 62, 500.
Solution:

Question 5.
The population of a village decreased by 12%. If the original population was 25,000, find the population after decrease?
Solution:

Question 6.
Out of a salary of Rs. 13,500,1 keep 1/3 as savings. Of the remaining money, I spend 50% on food and 20% on house rent. How much do I spend on food and house rent?
Solution:

Question 7.
A tank can hold 50 litres of water. At present, it is only 30% full. How many litres of water shall I put into the tank so that it becomes 50% full?
Solution:

Question 8.
In an election, there are a total of 80,000 voters and two candidates, A and B. 80% of the voters go to the polls out of which 60% vote for A. How many votes does B get.
Solution:

Question 9.
70% of our body weight is made up of water. Find the weight of water in the body of a person whose body weight is 56 kg.
Solution:

Question 10.
Only one-fifth of water is available in liquid form. This limited amount of water is replenished and used by man recurrently. Express this information as percent, showing :
(i) water available in liquid form.
(ii) water available in frozen form.
Solution:
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Question 11.
By weight, 90% of tomato and 78% of potato is water. Find :
(i) the weight of water in 25 kg of tomato.
(ii) the total quantity, by weight, of water in 90 kg of potato and 30 kg of tomato
(iii) the weight of potato which contains 39 kg of water.
Solution:

Percent Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Rohit’s age is 12 years and Geeta’s age is 15 years. Express :
(i) Rohit’s age as a percent of Geeta’s age.
(ii) Geeta’s age as a percent of Rohit’s age.
Solution:

Question 2.
A class has 30 boys and 20 girls. Find:
(i) the percentage of girls in the class
(ii) the percentage of boys in the class
(iii) percentage of number of boys as compared with number of girls.
Solution:

Question 3.
Mrs. Sharma went to the market with ₹ 800 in her purse. When she returned to her home, ₹ 240 were still left in her purse. What percent of her money did she spend in the market?
Solution:

Question 4.
In a mixture of two liquids A and B, 35% is liquid B. If the total quantity of the mixture is 20 kg, find the quantity of A, by weight.
Solution:

Question 5.
A girl got 375 marks out of 500 in the first term examination, 560 marks out of 800 in the second term examination and 840 marks out of 1200 in the third term examination. Find:
(i) her percentage score in the first term examination.
(ii) her percentage score in the second term examination.
(iii) her percentage score in the third term examination.
(iv) the total marks secured in all the three examinations.
(v) the total marks scored in all the three examinations.
(vi) her percentage score on the whole in all the three examinations.
Solution:

Question 6.
Out of his monthly income of ₹ 2,500; a man spends ₹ 1,750. What percent of his income does he save every month?
Solution:

Question 7.
Mr. Singh’s monthly salary is ₹ 15,000. This month he was promoted with an increment of ₹ 3,000 in his salary. Express his increment as a percent of his original salary.
Solution:

Question 8.
(i) The price of an article increased from ₹ 16 to ₹ 20 ; find the percentage increase.
(ii) The price of an article decreased from Rs 20 to Rs 16 ; find the percentage decrease.
Solution:

Question 9.
(i)) The salary of a man is ₹ 7,200 per month, which is now increased by 8%. Find his new salary per month.
(ii) The salary of Mr. Sahni is ₹ 8,400 per month, which is now decreased by 8%. Find his new salary per month.
Solution:

Question 10.
Find the percentage change from the first quantity to the second :
(i) ₹ 80, ₹ 120
(ii) 75 kg, 60 kg
(iii) 50 cm, 45 cm
Solution:

Question 11.
The original price of an article is ₹ 640. Find its new price when its price is :
(i) increased by 30%
(ii) decreased by 20%
Solution:

Question 12.
Find the number that is :
(i) 50% more than 48
(ii) 30% less than 70
Solution:

Question 13.
Evaluate :
(i) 8% of 900 – 12% of 750 + 20% of 165.
(ii) 70% of 70 + 90% of 90 – 120% of 120.
Solution:

Question 14.
Approximately 97.3% water on the earth is not fit for drinking. Find :
(i) the percentage of water on the earth that is fit for drinking.
(ii) The total volume of water available in certain part of the earth where there is 21,600 m3 of drinking water.
Solution:

Question 15.
Air is an important inexhaustible natural resource. It is essential for the survival of human beings, microbes, plants and animals. The following table shows the percentage of various gases in air.

(i) In 800 m3 of air, calculate the approximate quantities of nitrogen, oxygen and other gases.
(ii) If a certain quantity (by volume) of air contains 4,200 litres of oxygen, find the total quantity of air taken and the amount of nitrogen in it.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 34 Mean and Median

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 34 Mean and Median

Mean and Median Exercise 34A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the mean of :
(i) 7,10, 4 and 17
(ii) 12, 9, 6,11 and 17
(iii) 3, 1, 5, 4, 4 and 7
(iv) 7, 5, 0, 3, 0, 6, 0, 9, 1 and 4
(v) 2.1, 4.5, 5.2, 7.1 and 9.3
(vi) 5, 2.4, 6.2, 8.9, 4.1 and 3.4
Answer:

Question 2.
Find the mean of :
(i) first eight natural numbers
(ii) first six even natural numbers
(iii) first five odd natural numbers
(iv) all prime numbers upto 30
(v) all prime numbers between 20 and 40.
Answer:

Question 3.
Height (in cm) of 7 boys of a locality are 144 cm, 155 cm, 168 cm, 163 cm, 167 cm, 151 cm and 158 cm. Find their mean height.
Answer:

Question 4.
Find the mean of 35, 44, 31, 57, 38, 29, 26,36, 41 and 43.
Answer:

Question 5.
The mean of 18, 28, x, 32, 14 and 36 is 23. Find the value of x.
Answer:

Question 6.
If the mean of x, x + 2, x + 4, x + 6 and x + 8 is 13, find the value of x.
Answer:

Mean and Median Exercise 34B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the median of
(i) 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25
(ii) 3.2, 4.8, 5.6, 5.6, 7.3, 8.9 and 91
(iii) 17, 23, 36, 12, 18, 23, 40 and 20
(iv) 26, 33, 41, 18, 30, 22, 36, 45 and 24
(v) 80, 48, 66, 61, 75, 52, 45 and 70
Solution:

Question 2.
Find the mean and the median of :
(i) 1,3,4, 5, 9, 9 and 11
(ii) 10,12, 12, 15, 15, 17, 18, 18, 18 and 19
(iii) 2, 4, 5, 8, 10,13 and 14
(iv) 5, 8, 10, 11,13, 16, 19 and 20
(v) 1.2, 1.9, 2.2, 2.6 and 2.9
(vi) 0.5, 5.6, 3.8, 4.9, 2.7 and 4.4.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions