Category: ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.3

Question 1.
Factorise the following expressions using algebraic identities:
(i) x² – 12x + 36
(ii) 36p² – 60pq + 25q²
(iii) 9y² + 66xy + 121y²
(iv) a⁴ + 6a²b² + 9b⁴
(v) x² + \(\frac{1}{x^{2}}\) + 2
(vi) x² + x + \(\frac{1}{4}\)
Solution:

Factorise the following (2 to 13) expressions:
Question 2.
(i) 4p² – 9
(ii) 4x² – 169y²
Solution:

Question 3.
(i) 9x²y² – 25
(ii) 16x² – \(\frac{1}{144}\)
Solution:

Question 4.
(i) 20x² – 45y²
(ii) \(\frac{9}{16}\) – 25a²b²
Solution:

Question 5.
(i) (2a + 3b)² – 16c²
(ii) 1 – (b – c)²
Solution:

Question 6.
(i) 9 (x + y)² – x²
(ii) (2m + 3n)² – (3m + 2n)²
Solution:

Question 7.
(i) 25 (a + b)² – 16 (a – b)²
(ii) 9 (3x + 2)² – 4 (2x – 1)²
Solution:

Question 8.
(i) x³ – 25x
(ii) 63p²q² – 7
Solution:

Question 9.
(i) 32a²b – 72b³
(ii) 9 (a + b)³ – 25 (a + b)
Solution:

Question 10.
(i) x² – y² – 2y – 1
(ii) p²– 4pq + 4q² – r²
Solution:

Question 11.
(i) 9x² – y² + 4y – 4
(ii) 4a² – 4b² + 4a + 1
Solution:

Question 12.
(i) 625 – p⁴
(ii) 5y⁵ – 405y
Solution:

Question 13.
(i) x⁴ – y⁴ + x² – y²
(ii) 64a² – 9b² + 42bc – 49c²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.2

Factorise the following (1 to 11) polynomials:
Question 1.
(i) x² + xy – x – y
(ii) y² – yz – 5y + 5z
Solution:

Question 2.
(i) 5xy + 7y – 5y² – 7x
(ii) 5p² – 8pq – 10p + 16q
Solution:

Question 3.
(i) a²b – ab² + 3a – 3b
(ii) x³ – 3x² + x – 3
Solution:

Question 4.
(i) 6xy² – 3xy – 10y + 5
(ii) 3ax – 6ay – 8by + 4bx
Solution:

Question 5.
(i) x² + xy (1 + y) + y³
(ii) y² – xy (1 – x) – x³
Solution:

Question 6.
(i) ab² + (a – 1) b – 1
(ii) 2a – 4b – xa + 2bx
Solution:

Question 7.
(i) 5ph – 10qk + 2rph – 4qrk
(ii) x² – x(a + 2b) + 2a²
Solution:

Question 8.
(i) ab (x² + y²) – xy (a² + b²)
(ii) (ax + by)² + (bx – ay)²
Solution:

Question 9.
(i) a³ + ab(1 – 2a) – 2b²
(ii) 3x²y – 3xy + 12x – 12
Solution:

Question 10.
(i) a²b + ab² – abc – b²c + axy + bxy
(ii) ax² – bx² + ay² – by² + az² – bz²
Solution:

Question 11.
(i) x – 1 – (x – 1)² + ax – a
(ii) ax + a²x + aby + by – (ax + by)²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.1

Factorise the following (1 to 8) polynomials:
Question 1.
(i) 8xy³ + 12x²y²
(ii) 15ax³ – 9ax²
Solution:

Question 2.
(i) 21 py² – 56py
(ii) 4x³ – 6x²
Solution:

Question 3.
(i) 25abc² – 15a²b²c
(ii) x²yz + xy²z + xyz²
Solution:

Question 4.
(i) 8x³ – 6x² + 10x
(ii) 14mn + 22m – 62p
Solution:

Question 5.
(i) 18p²q² – 24pq² + 30p²q
(ii) 27a³b³ – 18a²b³ + 75a³b²
Solution:

Question 6.
(i) 15a (2p – 3p) – 106 (2p – 3q)
(ii) 3a (x² + y²) + 6b (x² + y²)
Solution:

Question 7.
(i) 6(x + 2y)³ + 8(x + 2y)²
(ii) 14(a – 3b)³ – 21p(a – 3b)
Solution:

Question 8.
10a (2p + q)³ – 15b (2p + q)² + 35(2p + q)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Check Your Progress

Question 1.
Add the following expressions:
(i) -5x²y + 3xy² – 7xy + 8, 12x²y – 5xy² + 3xy – 2
(ii) 9xy + 3yz – 5zx, 4yz + 9zx – 5y, -5xz + 2x – 5xy
Solution:

Question 2.
Subtract:
(i) 5a + 3b + 11c – 2 from 3a + 5b – 9c + 3
(ii) 10x² – 8y² + 5y – 3 from 8x² – 5xy + 2y² + 5x – 3y
Solution:

Question 3.
What must be added to 5x² – 3x + 1 to get 3x³ – 7x² + 8?
Solution:

Question 4.
Find the product of
(i) 3x²y and -4xy²
(ii) –\(\frac{4}{5}\)xy, \(\frac{5}{7}\)yz and –\(\frac{14}{9}\)zx
Solution:

Question 5.
Multiply:
(i) (3pq – 4p² + 5q² + 7) by -7pq
(ii) (\(\frac{3}{4}\)x²y – \(\frac{4}{5}\)xy + \(\frac{5}{6}\)xy²) by – 15xyz
Solution:

Question 6.
Multiply:
(i) (5x² + 4x – 2) by (3 – x – 4x²)
(ii) (7x² + 12xy – 9y²) by (3x² – 5xy + 3y²)
Solution:

Question 7.
Simplify the following expressions and evaluate them as directed:
(i) (3ab – 2a² + 5b²) x (2b² – 5ab + 3a²) + 8a³b – 7b⁴ for a = 1, b = -1
(ii) (1.7x – 2.5y) (2y + 3x + 4) – 7.8x² – 10y for x = 0, y = 1.
Solution:

Question 8.
Carry out the following divisions:
(i) 66pq²r³ ÷ 11qr²
(ii) (x³ + 2x² + 3x) ÷ 2x
Solution:

Question 9.
Divide 10x⁴ – 19x³ + 17x² + 15x – 42 by 2x² – 3x + 5.
Solution:

Question 10.
Using identities, find the following products:
(i) (3x + 4y) (3x + 4y)
(ii) \(\left(\frac{5}{2} a-b\right)\left(\frac{5}{2} a-b\right)\)
(iii) (3.5m – 1.5n) (3.5m + 1.5n)
(iv) (7xy – 2)(7xy + 7)
Solution:

Question 11.
Using suitable identities, evaluate the following:
(i) 105²
(ii) 97²
(iii) 201 × 199
(iv) 87² – 13²
(v) 105 × 107
Solution:

Question 12.
Prove that following:
(i) (a + b)² – (a – b)² + 4ab
(ii) (2a + 3b)² + (2a – 3b)² = 8a² + 18b²
Solution:

Question 13.
If x + \(\frac{1}{x}\) = 5, evaluate

Solution:

Question 14.
If a + b = 5 and a² + b² = 13, find ab.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A symbol which has a fixed value is called a ……….
(ii) A symbol which can be given various numerical values is called ……….. or ………
(iii) The various parts of an algebraic expression separated by + or – sign are called ………..
(iv) An algebraic expression having ………… terms is called a binomial.
(v) Each of the quantity (constant or literal) multiplied together to form a product is called a ………… of the product.
(vi) The terms having the same literal coefficients are called a ………… otherwise they are called …………
(vii) Degree of the polynomial is the greatest sum of the powers of ………… in each term.
(viii)An identity is equality which is true for ………… of variables in it.
(ix) (a + b)² = …………
(x) (x + a) (x + b) = x² + ………… + ab.
(xi) Dividend = ………… + remainder.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) An algebraic expression having only one term is called a monomial.
(ii) A symbol which has fixed value is called a literal.
(iii) The term of an algebraic expression having no literal factor is called its constant term,
(iv) In any term of an algebraic expression the constant part is called literal coefficient of the term.
(v) An algebraic expression is called polynomial if the powers of the variables involved in it in each term are non-negative integers.
(vi) 5x²y²z, 3x²zy², – \(\frac{4}{5}\) zx²y² are unlike terms.
(vii) 5x + \(\frac{2}{x}\) + 7 is a polynomial of degree 1.
(viii) 3x²y + 7x + 8y + 9 is a polynomial of degree 3.
(ix) Numerical coefficient of -7x³y is 7.
(x) An equation is true for all values of variables in it.
(xi) (a – b)² + 2ab = a² + b².
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 18):
Question 3.
The literal coefficient of -9xyz² is
(a) -9
(b) xy
(c) xyz²
(d) -9xy
Solution:

Question 4.
Which of the following algebraic expression is
(a) 3x² – 2x + 7
(b) \(\frac{5 x^{3}}{2 x}\) + 3x² + 8
(c) 3x + \(\frac{2}{x}\) + 7
(d) \(\sqrt{2}\)x² + \(\sqrt{3}\)x + \(\sqrt{6}\)
Solution:

Question 5.
Which of the following algebraic expressions is not a monomial?
(a) 3x × y × z
(b) -5pq
(c) 8m² × n ÷ 31
(d) 7x ÷ y – z
Solution:

Question 6.
Degree of the polynomial 7x²yz² + 6x³y²z² – 5x + 8y is
(a) 4
(b) 5
(c) 6
(d) 7
Solution:

Question 7.
a(b -c) + b(c – a) + c(a – b) is equal to
(a) ab + bc + ca
(b) 0
(c) 2(ab + bc + ca)
(d) none of these
Solution:

Question 8.
\(\frac{7}{5}\)xy – \(\frac{2}{3}\)xy + \(\frac{8}{9}\) xy is equal to

Solution:

Question 9.
(3p²qr³) × (-4p³q²r²) x (7pq³r) is equal to
(a) 84p⁶q⁶r⁶
(b) -84p⁶q⁶r⁶
(c) 84p⁶q⁵r⁶
(d) -84p⁶q⁵r⁶
Solution:

Question 10.
3m × (2m² – 5mn + 4n²) is equal to
(a) 6m³ + 15m²n – 12mn²
(b) 6m³ – 15m²n + 12mn²
(c) 6m³ – 15m²n – 12mn²
(d) 6m³ + 15m²n + 12mn²
Solution:

Question 11.
Volume of a rectangular box whose adjacent edges are 3x²y, 4y²z and 5z²x respectively is
(a) 60xyz
(b) 60x²y²z²
(c) 60x³y³z³
(d) none of these
Solution:

Question 12.
(x – 1) (x + 2) is equal to
(a) 2x + 3
(b) x² + 2x + 2
(c) x² + 3x + 2
(d) x² + 2x + 3
Solution:

Question 13.
If x + \(\frac{1}{x}\) = 2, then x² + \(\frac{1}{x^{2}}\) is equal to
(a) 4
(b) 2
(c) 0
(d) none of these
Solution:

Question 14.
If x² + y² = 9 and xy = 8, then x + y is equal to
(a) 25
(b) 5
(c) -5
(d) ±5
Solution:

Question 15.
(102)² – (98)² is equal to
(a) 200
(b) 400
(c) 600
(d) 800
Solution:

Question 16.
-50x³y²z² divided by -5xyz is equal to
(a) 10xyz
(b) 10x²yz
(c) -10xyz
(d) -10x²yz
Solution:

Question 17.
96 × 104 is equal to
(a) 9984
(b) 9974
(c) 9964
(d) none of these
Solution:

Question 18.
If the area of a rectangle is 24(x²yz + xy²z + xyz²) and its length is 8xyz, then its breadth is
(a) 3(x + y + z)
(b) 3xyz
(c) 3(x + y – z)
(d) none of these
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Using the identity (a + b) = a² + 2ab + b², derive the formula for (a + b + c)². Hence, find the value of (2x – 3y + 4z)².
Solution:

Question 2.
Using the product of algebraic expressions, find the formulas for (a + b)² and (a – b).
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.5

Question 1.
Using suitable identities, find the following products:
(i) (3x + 5) (3x + 5)
(ii) (9y – 5) (9y-5)
(iii) (4x + 11y) (4x – 11y)
(iv) \(\left(\frac{3}{2} m+\frac{2}{3} n\right)\left(\frac{3}{2} m-\frac{2}{3} n\right)\)
(v) \(\left(\frac{2}{a}+\frac{5}{b}\right)\left(\frac{2}{a}+\frac{5}{b}\right)\)
(vi) \(\left(\frac{p^{2}}{2}+\frac{2}{q^{2}}\right)\left(\frac{p^{2}}{2}-\frac{2}{q^{2}}\right)\)
Solution:

Question 2.
Using the identities, evaluate the following:
(i) 81²
(ii) 97²
(iii) 105²
(iv) 997²
(v) 6.1²
(vi) 496 × 504
(vii) 20.5 × 19.5
(viii) 9.62
Solution:

Question 3.
Find the following squares, using the identities:

Solution:

Question 4.
Using the identity, (x + a) (x + b) = x² + (a + b)x + ab, find the following products:
(i) (x + 7) (x + 3)
(ii) (3x + 4) (3x – 5)
(iii) (p² + 2q) (p² – 3q)
(iv) (abc + 3) (abc – 5)
Solution:

Question 5.
Using the identity, (x + a) (x + b) = x² + (a + b)x + ab, evaluate the following:
(i) 203 × 204
(ii) 8.2 × 8.7
(iii) 107 × 93
Solution:

Question 6.
Using the identity a² – b² = (a + b) (a – b), find
(i) 53² – 47²
(ii) (2.05)² – (0.95)²
(iii) (14.3)² – (5.7)²
Solution:

Question 7.
Simplify the following:
(i) (2x + 5y)² + (2x – 5y)²
(ii) \(\left(\frac{7}{2} a-\frac{5}{2} b\right)^{2}-\left(\frac{5}{2} a-\frac{7}{2} b\right)^{2}\)
(iii) (p² – q²r)² + 2p²q²r
Solution:

Question 8.
Show that:
(i) (4x + 7y)² – (4x – 7y)² = 112xy
(ii) \(\left(\frac{3}{7} p-\frac{7}{6} q\right)^{2}+p q=\frac{9}{49} p^{2}+\frac{49}{36} q^{2}\)
(iii) (p – q)(p + q) + (q – r)(q + r) + (r – p) (r + p) = 0
Solution:

Question 9.
If x + \(\frac{1}{x}\) = 2, evaluate:

Solution:

Question 10.
If x = \(\frac{1}{x}\) = 7, ecaluate:

Solution:

Question 11.
If x² + \(\frac{1}{x^{2}}\) = 23, evaluate:

Solution:

Question 12.
If a + b = 9 and = 10, find the value of a² + b².
Solution:

Question 13.
If a – b = 6 and a² + b² = 42, find the value of
Solution:

Question 14.
If a² + b² = 41 and ab = 4, find the values of
(i) a + b
(ii) a – b
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.4

Question 1.
Divide:
(i) – 39pq²r⁵ by – 24p³q³r
(ii) –\(\frac{3}{4}\)a²b³ by \(\frac{6}{7}\)a³b²
Solution:

Question 2.
Divide:
(i) 9x⁴ – 8x³ – 12x + 3 by 3x
(ii) 14p²q³ – 32p³q² + 15pq² – 22p + 18q by – 2p²q.
Solution:

Question 3.
Divide:
(i) 6x² + 13x + 5 by 2x + 1
(ii) 1 + y³ by 1 + y
(iii) 5 + x – 2x² by x + 1
(iv) x³ – 6x² + 12x – 8 by x – 2
Solution:

Question 4.
Divide:
(i) 6x³ + x² – 26x – 25 by 3x – 7
(ii) m³ – 6m² + 7 by m – 1
Solution:

Question 5.
Divide:
(i) a³ + 2a² + 2a + 1 by + a² + a + 1
(ii) 12x³ – 17x² + 26x – 18 by 3x² – 2x + 5
Solution:

Question 6.
If the area of a rectangle is 8x² – 45y² + 18xy and one of its sides is 4x + 15y, find the length of the adjacent side.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.3

Question 1.
Multiply:
(i) (5x – 2) by (3x + 4)
(ii) (ax + b) by (cx + d)
(iii) (4p – 7) by (2 – 3p)
(iv) (2x² + 3) by (3x – 5)
(v) (1.5a – 2.5b) by (1.5a + 2.56)
(vi) \(\left(\frac{3}{7} p^{2}+4 q^{2}\right) \text { by } 7\left(p^{2}-\frac{3}{4} q^{2}\right)\)
Solution:

Question 2.
Multiply:
(i) (x – 2y + 3) by (x + 2y)
(ii) (3 – 5x + 2 × 2) by (4x – 5)
Solution:

Question 3.
Multiply:
(i) (3x² – 2x – 1) by (2x² + x – 5)
(ii) (2 – 3y – 5y²) by (2y – 1 + 3y²)
Solution:

Question 4.
Simplify:
(i) (x² + 3) (x – 3) + 9
(ii) (x + 3) (x – 3) (x + 4) (x – 4)
(iii) (x + 5) (x + 6) (x + 7)
(iv) (p + q – 2r) (2p – q + r) – 4qr
(v) (p + q) (r + s) + (p – q)(r – s) – 2(pr + qs)
(vi) (x + y + z) (x – y + z) + (x + y – z) (-x + y + z) – 4zx
Solution:

Question 5.
If two adjacent sides of a rectangle are 5x² + 25xy + 4y² and 2x² – 2xy + 3y², find its area.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.2

Question 1.
Find the product of:
(i) 4x³ and -3xy
(ii) 2xyz and 0
(iii) –\(\frac{2}{3}\)p²q, \(\frac{3}{4}\)pq² and 5pqr
(iv) -7ab,-3a³ and –\(\frac{2}{7}\)ab²
(v) –\(\frac{1}{2}\)x² – \(\frac{3}{5}\)xy, \(\frac{2}{3}\)yz and \(\frac{5}{7}\)xyz
Solution:

Question 2.
Multiply:
(i) (3x – 5y + 7z) by – 3xyz
(ii) (2p² – 3pq + 5q² + 5) by – 2pq
(iii) (\(\frac{2}{3}\)a²b – \(\frac{4}{5}\)ab² + \(\frac{2}{7}\)ab + 3) by 35ab
(iv) (4x² – 10xy + 7y² – 8x + 4y + 3) by 3xy
Solution:

Question 3.
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
(i) (p²q, pq²)
(ii) (5xy, 7xy²)
Solution:

Question 4.
Find the volume of rectangular boxes with the following length, breadth and height respectively:
(i) 5ab, 3a²b, 7a⁴b²
(ii) 2pq, 4q², 8rp
Solution:

Question 5.
Simplify the following expressions and evaluate them as directed:
(i) x²(3 – 2x + x²) for x = 1; x = -1; x = \(\frac{2}{3}\) and x = –\(\frac{1}{2}\)
(ii) 5xy(3x + 4y – 7) – 3y(xy – x² + 9) – 8 for x = 2, y = -1
Solution:

Question 6.
Add the following:
(i) 4p(2 – p²) and 8p³ – 3p
(ii) 7xy(8x + 2y – 3) and 4xy²(3y – 7x + 8)
Solution:

Question 7.
Subtract:
(i) 6x(x – y + z)- 3y(x + y – z) from 2z(-x + y + z)
(ii) 7xy(x² -2xy + 3y²) – 8x(x²y – 4xy + 7xy²) from 3y(4x²y – 5xy + 8xy²)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.1

Question 1.
Identify the terms, their numerical as well as literal coefficients in each of the following expressions:
(i) 12x²yz – 4xy²
(ii) 8 + mn + nl – lm
Solution:

Question 2.
Identify monomials, binomials, and trinomials from the following algebraic expressions :
(i) 5p × q × r²
(ii) 3x² + y ÷ 2z
(iii) -3 + 7x²
(iv) \(\frac{5 a^{2}-3 b^{2}+c}{2}\)
(v) 7x⁵ – \(\frac{3 x}{y}\)
(vi) 5p ÷ 3q – 3p² × q²
Solution:

Question 3.
Identify which of the following expressions are polynomials. If so, write their degrees.
(i) \(\frac{2}{5}\)x⁴ – \(\sqrt{3}\)x² + 5x – 1
(ii) 7x³ – \(\frac{3}{x^{2}}\) + \(\sqrt{5}\)
(iii) 4a³b² – 3ab⁴ + 5ab + \(\frac{2}{3}\)
(iv) 2x²y – \(\frac{3}{x y}\) + 5y³ + \(\sqrt{3}\)
Solution:

Question 4.
Add the following expressions:
(i) ab – bv, bv – ca, ca – ab
(ii) 5p²q² + 4pq + 7,3 + 9pq – 2p²q
(iii) l² + m² + n², lm + mn, mn + nl, nl + lm
(iv) 4x³ – 7x² + 9, 3x² – 5x + 4, 7x³ – 11x + 1, 6x² – 13x
Solution:

Question 5.
Subtract:
(i) 8a + 3ab – 2b + 7 from 14a – 5ab + 7b – 5
(ii) 8xy + 4yz + 5zx from 12xy – 3yz – 4zx + 5xyz
(iii) 4p²q – 3pq + 5pq² – 8p + 7q -10 from 18 – 3p – 11q + 5pq – 2pq² + 5p²q
Solution:

Question 6.
Subtract the sum of 3x² + 5xy + 7y² + 3 and 2x² – 4xy – 3y² + 7 from 9x² – 8xy + 11y²
Solution:

Question 7.
What must be subtracted from 3a² – 5ab – 2b² – 3 to get 5a² – 7ab – 3b² + 3a ?
Solution:

Question 8.
The perimeter of a triangle is 7p² – 5p + 11 and two of its sides are p² + 2p – 1 and 3p² – 6p + 3. Find the third side of the triangle.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Check Your Progress

Question 1.
Match each of the entries in column I with the appropriate entry in column II.

Solution:

Question 2.
(i) From the following table, determines and q if x and y vary directly:

(ii) From the following table, determine a and b if x and y vary inversely:

Solution:

Question 3.
It rained 80 mm in the first 20 days of April. What would be the total rainfall in April?
Solution:

Question 4.
Mamta earns ₹540 for a working week of 48 hours. If she was absent for 6 hours, how much did she earn?
Solution:

Question 5.
Navjot can do a piece of work in 6 days working 10 hours per day. In how many days can he do the same work if he increases his working hours by 2 hours per day?
Solution:

Question 6.
Sharmila has enough money to buy 24 bananas at the rate of ₹ 1·50 per banana. How many bananas she can buy if the price of each orange is decreased by 30 paise?
Solution:

Question 7.
A fort has rations for 180 soldiers for 40 days. After 10 days, 30 soldiers leave the fort. Find the total number of days for which the food will last.
Solution:

Question 8.
There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?
Solution:

Question 9.
If 4 goats or 6 sheep can graze a field in 40 days, how many days will 4 goats and 14 sheep take to graze the same field?
Solution:

Question 10.
A tap can fill a tank in 20 hours, while the other can empty it in 30 hours. The tank is empty and if both taps are opened together, how long will it take for the tank to be half full?
Solution:

Question 11.
Three ants separately can gobble a grasshopper in 3,4, and 6 days respectively. How many days will they take together to finish off the poor chap? If the grasshopper weighs 63 gram, find the share of each.
Solution:

Question 12.
A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days A alone will do the same work?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths