Category: ICSE

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 6 The Circulatory System

Selina Concise Biology Class 6 ICSE Solutions

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 5 Respiratory System

Selina Concise Biology Class 6 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Profit, Loss and Discount Exercise 8A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Megha bought 10 note-books for Rs.40 and sold them at Rs.4.75 per note-book. Find, her gain percent.
Solution:

Question 2.
A fruit-seller buys oranges at 4 for Rs.3 and sells them at 3 for Rs.4 Find his profit percent.
Solution:

Question 3.
A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs.108. Find ;
(i) his gain as percent;
(ii) the number of articles sold to make a profit of Rs.75.
Solution:

Question 4.
A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycles for Rs. 207. Find his gain or loss percent.
Solution:

Question 5.
An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportations, etc. ; find he loss or the gain as percent.
Solution:

Question 6.
Mohit sold a T.V. for Rs. 3,600 ; gaining one-sixth of its selling price. Find :
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.
Solution:

Question 7.
By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find :
(i) the loss incured
(ii) the cost price of the goods
(iii) the loss as percent.
Solution:

Question 8.
The selling price of a sofa-set is \(\frac { 4 }{ 5 }\) times of its cost price. Find the gain or the loss as percent.
Solution:

Question 9.
The cost price of an article is \(\frac { 4 }{ 5 }\) times of its selling price. Find the loss or the gain as percent.
Solution:

Question 10.
A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?
Solution:

Question 11.
The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Solution:

Question 12.
The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.
Solution:

Question 13.
A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.
Solution:

Question 14.
A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :
(i) its cc price;
(ii) the loss percent.
Solution:

Question 15.
A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;
(i) its cost price;
(ii) the profit percent.
Solution:

Profit, Loss and Discount Exercise 8B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the selling price, if:
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution:

Question 2.
Find the cost price, if :
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution:

Question 3.
By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
Solution:

Question 4.
By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
Solution:

Question 5.
Find the selling price, if :
(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20
(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%
Solution:

Question 6.
If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5%?
Solution:

Question 7.
A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16%?
Solution:

Question 8.
By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent ; if he sells the same sofa-set for Rs.3150.
Solution:

Question 9.
Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution:

Question 10.
A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player.
(iii) the total C.P. of both.
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole
Solution:

Question 11.
Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh
Solution:

Question 12.
John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it ?
Solution:

Profit, Loss and Discount Exercise 8C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A stationer buys pens at 5 for Rs.28 and sells them at a profit of 25 %. How much should a customer pay; if he buys
(i) only one pen ;
(ii) three pens ?
Solution:

Question 2.
A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :
(i) C.P. of 4 oranges,
(ii) C.P. of one orange.
(iii) S.P. of one orange.
(iv) profit made by selling one orange.
(v) number of oranges brought and sold in order to gain Rs. 24.
Solution:

Question 3.
A man sells 12 articles for Rs. 80 gaining 33\(\frac { 1 }{ 3 }\) %. Find the number of articles bought by the man for Rs. 90.
Solution:

Question 4.
The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
Solution:

Question 5.
The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
Solution:

Question 6.
By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
Solution:

Question 7.
A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
If he desires a profit of 12% on the whole ; find :
(i) the selling price of the rest of the rice ;
(ii) the percentage profit on the rest of the rice.
Solution:

Question 8.
Mohan bought a certain number of note-books for Rs.600. He sold \(\frac { 1 }{ 4 }\) of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole ?
Solution:

Question 9.
Raju sells a watch at 5% profit. Had he sold it for Rs.24 more ; he would have gained 11%. Find the cost price of the watch.
Solution:

Question 10.
A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
Solution:

Question 11.
Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs.36 more; she would have gained 20%. Find the cost price of the article.
Solution:

Profit, Loss and Discount Exercise 8D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
An article is marked for Rs. 1,300 and is sold for Rs. 1,144 ; find the discount percent.
Solution:

Question 2.
The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution:

Question 3.
A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400 ; find the discount given and the selling price of the watch.
Solution:

Question 4.
A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution:

Question 5.
A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :
(i) the marked price of the article.
(ii) the selling price, if he sells the articles at 10 percent discount.
(iii) the percentage discount given by him, if he sells the article for Rs.496.80
Solution:

Question 6.
The list price of an article is Rs.800 and is available at a discount of 15 percent. Find :
(i) selling price of the article ;
(ii) cost price of the article, if a profit of 13\(\frac { 1 }{ 3 }\) % is made on selling it.
Solution:

Question 7.
An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution:

Question 8.
By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440 ; find :
(i) the marked price of the article.
(ii) the cost price of the article.
Solution:

Question 9.
A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
Solution:

Question 10.
A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.
Solution:

Question 11.
At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution:

Question 12.
The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.
Solution:

Question 13.
Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?
Solution:

Question 14.
The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:
(i) Its marked price
(ii) its selling price
(iii) the profit percent.
Solution:

Question 15.
Find a single discount (as percent) equivalent to following successive discounts:
(i) 20% and 12%
(ii) 10%, 20% and 20%
(iii) 20%, 10% and 5%
Solution:

Question 16.
Find the single discount (as percent) equivalent to successive discounts of:
(i) 80% and 80%
(ii) 60% and 60%
(iii) 60% and 80%
Solution:

Profit, Loss and Discount Exercise 8E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Rajat purchases a wrist-watch costing Rs. 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.
Solution:

Question 2.
Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution:

Question 3.
The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.
Solution:

Question 4.
Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution:

Question 5.
The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V. ?
Solution:

Question 6.
The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution:

Question 7.
A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution:

Question 8.
When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V. ; Mrs. Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution:

Question 9.
A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.
Solution:

Profit, Loss and Discount Exercise 8F – Selina Concise Mathematics Class 8 ICSE Solutions

[In this exercise, all the prices are excluding tax/VAT unless specified]
Question 1.
A shopkeeper buys an article for ₹ 8,000 and sells it for ₹ 10,000. If the rate of tax under VAT is 10%, find :
(i) tax paid by the shopkeeper
(ii) tax charged by the shopkeeper
(iii) VAT paid by the shopkeeper
Solution:

Question 2.
A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?
Solution:

Question 3.
The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.
Solution:

Question 4.
A buys some goods for ₹ 4,000 and sold them to B for ₹ 5,000. B sold these goods to C for ₹ 6,000. If the rate of tax (under VAT) at each stage is 5%, find :
(i) VAT paid by A
(ii) VAT paid by B
Solution:

Question 5.
A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :
(i) tax paid by A
(ii) tax charged by A
(iii) VAT paid by A
Solution:

Question 6.
A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.
Solution:

Question 7.
A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.
Solution:

Question 8.
A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.
Solution:

Question 9.
The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:
(i) distributor
(ii) trader
Solution:

Question 10.
The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 3 Cell – The Structure and Functions

Selina Concise Biology Class 6 ICSE Solutions

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 3 Cell – The Structure and Functions

Selina Concise Biology Class 6 ICSE Solutions

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 2 The Flower

Selina Concise Biology Class 6 ICSE Solutions

Selina Publishers Concise Biology Class 6 ICSE Solutions Chapter 1 The Leaf

Selina Concise Biology Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Data Handling Exercise 21A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Consider the following numbers :
68, 76, 63, 75, 93, 83, 70, 115, 82, 105, 90, 103, 92, 52, 99, 73, 75, 63, 77 and 71.
(i) Arrange these numbers in ascending order.
(ii) What the range of these numbers?
Solution:

Question 2.
Represent the following data in the form of a frequency distribution table :
16, 17, 21, 20, 16, 20, 16, 18, 17, 21, 17, 18, 19, 17, 15, 15, 19, 19, 18, 17, 17, 15, 15, 16, 17, 17, 19, 18, 17, 16, 15, 20, 16, 17, 19, 18, 19, 16, 21 and 17.
Solution:

Question 3.
A die was thrown 20 times and following scores were recorded.
2, 1, 5, 2, 4, 3, 6, 1, 4, 2, 5, 1, 6, 2, 6, 3, 5, 4, 1 and 3.
Prepare a frequency table for the scores.
Solution:

Question 4.
Following data shows the weekly wages (in ₹) of 10 workers in a factory.
3500, 4250, 4000, 4250, 4000, 3750, 4750, 4000, 4250 and 4000
(i) Prepare a frequency distribution table.
(ii) What is the range of wages (in ₹)?
(iii) How many workers are getting the maximum wages?
Solution:

Question 5.
The marks obtained by 40 students of a class are given below :
80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40,20, 80, 90, 50, 80, 60, 70, 40, 50, 60, 90, 60, 40, 40, 60 and 60
(i) Construct a frequency distribution table.
(ii) Find how many students have marks equal to or more than 70?
(iii) How many students obtained marks below 40?
Solution:

Question 6.
Arrange the following data in descending order:
3.3, 3.2, 3.1, 3.7, 3.6, 4.0, 3.5, 3.9, 3.8, 4.1, 3.5, 3.8, 3.7, 3.9 and 3.4.
(i) Determine the range.
(ii) How many numbers are less than 3.5?
(iii) How many numbers are 3.8 or above?
Solution:

Data Handling Exercise 21B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the mean of 53, 61, 60, 67 and 64.
Solution:

Question 2.
Find the mean of first six natural numbers.
Solution:

Question 3.
Find the mean of first ten odd natural numbers.
Solution:

Question 4.
Find the mean of all factors of 10.
Solution:

Question 5.
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
Solution:

Question 6.
If different values of variable x are 19.8,15.4,13.7,11.71,11.8, 12.6,12.8,18.6,20.5 and 2.1, find the mean.
Solution:

Question 7.
The mean of a certain number of observations is 32. Find the resulting mean, if each observation is,
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%
Solution:

Question 8.
The pocket expenses (per day) of Anuj, during a certain week, from monday to Saturday were ₹85.40, ₹88.00, ₹86.50, ₹84.75, ₹82.60 and ₹87.25. Find the mean pocket expenses per day.
Solution:

Question 9.
If the mean of 8, 10, 7, x + 2 and 6 is 9, find the value of x.
Solution:

Question 10.
Find the mean of first six multiples of 3.
Solution:

Question 11.
Find the mean of first five prime numbers.
Solution:

Question 12.
The mean of six numbers :x-5,x- 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
Solution:

Question 13.
Find the mean of squares of first five whole numbers.
Solution:

Question 14.
If the mean of 6, 4, 7, p and 10 is 8, find the value of p.
Solution:

Question 15.
Find the mean of first six multiples of 5.
Solution:

Question 16.
The rainfall (in mm) in a city on 7 days of a certain week is recorded as follows

Find the total and average (mean) rainfall for the week.
Solution:

Question 17.
The mean of marks scored by 100 students was found to be 40, later on it was discovered that a score of 53 was misread as 83. Find the correct mean.
Solution:

Question 18.
The mean of five numbers is 27. If one number is excluded, the mean of remaining numbers is 25. Find the excluded number.
Solution:

Question 19.
The mean of 5 numbers is 27. If one new number is included, the new mean is 25. Find the included number.
Solution:

Question 20.
Mean of 5 numbers is 20 and mean of other 5 numbers is 30. Find the mean of all the 10 numbers taken together.
Solution:

Question 21.
Find the median of:
(i) 5,7, 9, 11, 15, 17,2, 23 and 19
(ii) 9, 3, 20, 13, 0, 7 and 10
(iii) 18, 19, 20, 23, 22, 20, 17, 19, 25 and 21
(iv) 3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9 and 7.6.
Solution:

Question 22.
Find the mean and the mode for the following data :

Solution:

Question 23.
Find the mode of:
(i) 5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 3
(ii) 7, 7, 8, 10, 10, 11, 10, 13, 14
Solution:

Question 24.
Find the mode of :

Solution:

Question 25.
The heights (in cm) of 8 girls of a class are 140,142,135,133,137,150,148 and 138 respectively. Find the mean height of these girls and their median height.
Solution:

Question 26.
Find the mean, the median and the mode of:
(i) 12, 24, 24, 12, 30 and 12
(ii) 21, 24, 21, 6, 15, 18, 21, 45, 9, 6, 27 and 15.
Solution:

Question 27.
The following table shows the market positions of some brands of soap.
Draw a suitable bar graph :

Solution:

Question 28.
The birth rate per thousand of different countries over a particular period of time is shown below.

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Mensuration Exercise 20A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The length and the breadth of a rectangular plot are 135 m and 65 m. Find, its perimeter and the cost of fencing it at the rate of ₹60 per m.
Solution:

Question 2.
The length and breadth of a rectangular field are in the ratio 7 : 4. If its perimeter is 440 m, find its length and breadth. Also, find the cost of fencing it @ ₹150 per m.
Solution:

Question 3.
The length of a rectangular field is 30 m and its diagonal is 34 m. Find the breadth of the field and its perimeter.
Solution:

Question 4.
The diagonal of a square is 12\(\sqrt { 2 } \) cm. Find its perimeter.
Solution:

Question 5.
Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 dm.
Solution:

Question 6.
Find the perimeter of a rectangle with length = 24 cm and diagonal = 25 cm
Solution:

Question 7.
The length and breadth of rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at the rate of ₹48 per metre is ₹19,200, find its length and breadth.
Solution:

Question 8.
A wire is in the shape of square of side 20 cm. If the wire is bent into a rectangle of length 24 cm, find its breadth.
Solution:

Question 9.
If P = perimeter of a rectangle, l= its length and b = its breadth find :
(i) P, if l = 38 cm and b = 27 cm
(ii) b, if P = 88 cm and l = 24 cm
(iii) l, if P = 96 m and b = 28 m
Solution:

Question 10.
The cost of fencing a square field at the rate of
Cost of fencing 440 m = ₹150 x 440 = ₹75 per meter is
Cost of fencing 440 m = ₹150 x 440 = ₹67,500. Find the perimeter and the side of the square field.
Solution:

Question 11.
The length and the breadth of a rectangle are 36 cm and 28 cm. If its perimeter is equal to the perimeter of a square, find the side of the square.
Solution:

Question 12.
The radius of a circle is 21 cm. Find the circumference (Take π = 3 \(\frac { 1 }{ 7 }\) ).
Solution:

Question 13.
The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = \(\frac { 22 }{ 7 }\)
Solution:

Question 14.
The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take n = \(\frac { 22 }{ 7 }\))
Solution:

Question 15.
The radii of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π = \(\frac { 22 }{ 7 }\))
Solution:

Question 16.
The diameter of a circle is 42 cm, find its perimeter. If the perimeter of the circle is doubled, what will be the radius of the new circle. (Take π = \(\frac { 22 }{ 7 }\) )
Solution:

Question 17.
The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.
Solution:

Question 18.
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radii 15 cm and 8 cm.
Solution:

Question 19.
Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm and 18 cm.
Solution:

Question 20.
The circumference of a circle is eigth time the circumference of the circle with radius 12 cm. Find its diameter.
Solution:

Question 21.
The radii of two circles are in the ratio 3 : 5, find the ratio between their circumferences.
Solution:

Question 22.
The circumferences of two circles are in the ratio 5 : 7, find the ratio between their radii.
Solution:

Question 23.
The perimeters of two squares are in the ratio 8:15, find the ratio between the lengths of their sides.
Solution:

Question 24.
The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters.
Solution:

Question 25.
Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.
Solution:

Mensuration Exercise 20B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the area of a rectangle whose length and breadth are 25 cm and 16 cm.
Solution:

Question 2.
The diagonal of a rectangular board is 1 m and its length is 96 cm. Find the area of the board.
Solution:

Question 3.
The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m², find
(i) its perimeter
(ii) cost of fencing it at the rate of ₹40 per meter.
Solution:

Question 4.
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
Solution:

Question 5.
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m².
Solution:

Question 6.
Find the area of the square whose perimeter is 56 cm.
Solution:

Question 7.
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m² find the area of the lawn.
Solution:

Question 8.
For each figure, given below, find the area of shaded region : (All measurements are in cm)

Solution:

Question 9.
One side of a parallelogram is 20 cm and its distance from the opposite side is 16 cm. Find the area of the parallelogram.
Solution:

Question 10.
The base of a parallelogram is thrice it height. If its area is 768 cm², find the base and the height of the parallelogram.
Solution:

Question 11.
Find the area of the rhombus, if its diagonals are 30 cm and 24 cm.
Solution:

Question 12.
If the area of a rhombus is 112 cm² and one of its diagonals is 14 cm, find its other diagonal.
Solution:

Question 13.
One side of a parallelogram is 18 cm and its area is 153 cm². Find the distance of the given side from its opposite side.
Solution:

Question 14.
The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.
Solution:

Question 15.
The area of a rhombus is 84 cm2 and its perimeter is 56 cm. Find its height.
Solution:

Question 16.
Find the area of a triangle whose base is 30 cm and height is 18 cm.
Solution:

Question 17.
Find the height of a triangle whose base is 18 cm and area is 270 cm².
Solution:

Question 18.
The area of a right-angled triangle is 160 cm². If its one leg is 16 cm long, find the length of the other leg.
Solution:

Question 19.
Find the area of a right-angled triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long.
Solution:

Question 20.
Find the area of an equilateral triangle whose each side is 16 cm. (Take \(\sqrt { 3 } \)= 1.73)
Solution:

Question 21.
The sides of a triangle are 21 cm, 17 cm and 10 cm. Find its area.
Solution:

Question 22.
Find the area of an isosceles triangle whose base is 16 cm and length of each of the equal sides is 10 cm.
Solution:

Question 23.
Find the base of a triangle whose area is 360 cm²and height is 24 cm.
Solution:

Question 24.
The legs of a right-angled triangle are in the ratio 4 :3 and its area is 4056 cm². Find the length of its legs.
Solution:

Question 25.
The area of an equilateral triangle is (64 x \(\sqrt { 3 } \) ) cm²– Find the length of each side of the triangle.
Solution:

Question 26.
The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.
Solution:

Question 27.
The diameter of a circle is 20 cm. Taking π = 3.14, find the circumference and its area.
Solution:

Question 28.
The circumference of a circle exceeds its diameter by 18 cm. Find the radius of the circle.
Solution:

Question 29.
The ratio between the radii of two circles is 5 : 7. Find the ratio between their :
(i) circumference
(ii) areas
Solution:

Question 30.
The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radii
(ii) diameters
(iii) circumference
Solution:

Question 31.
A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.
Solution:

Question 32.
The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.
Solution:

Question 33.
The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheel.
Solution:

Question 34.
The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel one kilometre?
Solution:

Question 35.
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm². Find the length of the wire. If the same wire is bent to a largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
Solution:

Question 36.
A wire is along the boundary of a circle with radius 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.
Solution:

Question 37.
The length and the breadth of a rectangular paper are 35 cm and 22 cm. Find the area of the largest circle which can be cut out of this paper.
Solution:

Question 38.
From each comer of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 16 Understanding Shapes (Including Polygons)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 16 Understanding Shapes (Including Polygons)

Understanding Shapes Exercise 16A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
State which of the following are polygons :

If the given figure is a polygon, name it as convex or concave.
Solution:

Question 2.
Calculate the sum of angles of a polygon with :
(i) 10 sides
(ii) 12 sides
(iii) 20 sides
(iv) 25 sides
Solution:

Question 3.
Find the number of sides in a polygon if the sum of its interior angles is :
(i) 900°
(ii) 1620°
(iii) 16 right-angles
(iv) 32 right-angles.
Solution:

Question 4.
Is it possible to have a polygon ; whose sum of interior angles is :
(i) 870°
(ii) 2340°
(iii) 7 right-angles
(iv) 4500°
Solution:

Question 5.
(i) If all the angles of a hexagon are equal ; find the measure of each angle.
(ii) If all the angles of a 14-sided figure are equal ; find the measure of each angle.
Solution:

Question 6.
Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with :
(i) 7 sides
(ii) 10 sides
(iii) 250 sides.
Solution:

Question 7.
The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x – 1)°, (10x + 2)°, (8x + 2)° (9x – 3)°, (5x + 4)° and (12x + 6)° ; find each exterior angle.
Solution:

Question 8.
The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.
Solution:

Question 9.
Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.
Solution:

Question 10.
The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.

(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E
(iii) Find angles B, C and D.
Solution:

Question 11.
Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.
Solution:

Question 12.
In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.
Solution:

Question 13.
the angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°. Find x.
Solution:

Question 14.
In a pentagon, two angles are 40° and 60°, and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.
Solution:

Understanding Shapes Exercise 16B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Fill in the blanks :
In case of regular polygon, with :

Solution:

Question 2.
Find the number of sides in a regular polygon, if its each interior angle is :
(i) 160°
(ii) 135°
(iii) \(1\frac { 1 }{ 5 }\) of a right-angle
Solution:

Question 3.
Find the number of sides in a regular polygon, if its each exterior angle is :
(i) \(\frac { 1 }{ 3 }\) of a right angle
(ii) two-fifth of a right-angle.
Solution:

Question 4.
Is it possible to have a regular polygon whose each interior angle is :
(i) 170°
(ii) 138°
Solution:

Question 5.
Is it possible to have a regular polygon whose each exterior angle is :
(i) 80°
(ii) 40% of a right angle.
Solution:
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Question 6.
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
Solution:

Question 7.
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
Solution:

Question 8.
The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :
(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.
Solution:

Question 9.
The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :
(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon
Solution:

Question 10.
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
Solution:

Question 11.
The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.
Solution:

Question 12.
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
Solution:

Question 13.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
Solution:

Question 14.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
Solution:

Question 15.
The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. Find the value of n.
Solution:

Question 16.
If the difference between the exterior angle of a n sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Solution:

Question 17.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Solution:

Question 18.
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
Solution:

Question 19.
Calculate the number of sides of a regular polygon, if:
(i) its interior angle is five times its exterior angle.
(ii) the ratio between its exterior angle and interior angle is 2 : 7.
(iii) its exterior angle exceeds its interior angle by 60°.
Solution:

Question 20.
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
Solution:

Understanding Shapes Exercise 16C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:

Question 3.
Angles of a quadrilateral are (4x)°, 5(x + 2)°, (7x – 20)° and 6(x + 3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C

Solution:

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD
Solution:

Question 6.
From the following figure find ;
(i) x
(ii) ∠ABC
(iii) ∠ACD
Solution:

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a + 2)° and ∠B = 2(2a + 7)°.
Calculate ∠A.
Solution:

Question 8.
In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.

Solution:

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.
Solution:

Question 11.
Use the informations given in the following figure to find the value of x.

Solution:

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Solution:

Question 13.
Use the following figure to find the value of x

Solution:

Question 14.
ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC = 90°.
Solution:

Question 15.
In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively. Show that:
∠AOB = \(\frac { 1 }{ 2 }\) (∠C + ∠D)
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids (Representing 3-D in 2-D)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids (Representing 3-D in 2-D)

Recognition of solids Exercise 18 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Identify the nets which can be used to form cubes

Solution:

Question 2.
Draw at least three different nets for making cube.
Solution:

Question 3.
The figure, given below, shows shadows of some 3D objects, when seen under the lamp of an overhead projector :

In each case, name the object.
Solution:

Question 4.
Using Euler’s formula, find the values of a, b, c and d.

Solution:

Question 5.
Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
Below are given two nets to make dice (cube), the numbers inserted in each square indicate the number of dots in it.

Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.
Solution:

Question 6.
The following figures represent nets of some solids. Name the solids

Solution:

Question 7.
Draw a map of your class room using proper scale and symbols for different objects.
Solution:

Question 8.
Draw a map of your school compound using proper scale and symbols for various features like play ground, main building, garden, etc.
Solution:

Question 9.
In the map of India, the distance between two cities is 13.8 cm.
Taking scale : 1 cm = 12 km, find the actual distance between these two cities.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions