# NCERT Solutions for Class 7 Mathematics Chapter 8 - Comparing Quantities

##### Question 1:

Find the percentage of children of different heights for the following data:

Respective number of children of different heights are out of 100 children.
Therefore percentage of children of respective height are in the following table:

##### Question 2:

Respective number of shoes of different sizes are out of 100 shoes.
Therefore percentage of each shoe sizes is in the following table:

##### Question 3:

A collection of 10 chips is given with different colours:

Fill the table and find the percentage of chips of each colour.

As we know that if total number on adding does not give 100, then we convert the fraction to an equivalent fraction with denominator 100.
So; given table is completed as follows:

##### Question 4:

Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What is the percentage of bangles of each type? Can you put it in the tabular form as done is the above example?

##### Question 5:

Look at the example below and discuss which is better for comparision.
In the atmosphere, 1 g of air contains:

In atmosphere the quantity of air contained in per cent is better for comparison at a glance which shows that out of 100 parts of air; 78 parts are of nitrogen, 21 parts are of oxygen and 1 part is of other gases.

##### Question 6:

Look at the example below and discuss which is better for comparison:
A shirt has:

Quantity of blending of cotton and polyster in a shirt is easy to understand in terms of percentage.
It shows that out of 100 parts of a shirt; 60 parts are of cotton and 40 parts are of polyster.

##### Question 7:

Convert the following to per cents:

##### Question 8:

Convert the following to per cents:
3.5

##### Question 9:

Convert the following to per cents:

##### Question 10:

Convert the following to per cents:

= 1 × 100%
= 100%

##### Question 11:

Convert the following to per cents:
0.05

##### Question 12:

Out of 32 students, 8 are absent. What per cent of the students are absent?

Out of 32 students; number of absentee = 8
Therefore, out of 100, number of absentee

##### Question 13:

There are 25 radios, 16 of them are out of order. What per cent of radios are out of order?

If there are 25 radios then the number of radios which are out of order = 16 Therefore, from 100 radios, the radios which are out of order

##### Question 14:

A shop has 500 parts, out of which 5 are defective. What per cent are defective?

Out of 500 parts; defective parts are 5
Therefore, out of 100 parts, defective parts

##### Question 15:

There are 120 voters, 90 of them voted yes. What per cent voted yes?

Out of 120 voters, voters voted yes are 90.
Therefore, out of 100 voters, voters voted yes

##### Question 16:

35% + _________ % = 100%

65

##### Question 17:

64% + 20% + _________ % = 100%

16

##### Question 18:

45% = 100% – _________ %

55

##### Question 19:

70% = _________ % – 30%.

100

##### Question 20:

If 65% of students in a class have a bicycle, what per cent of the student do not have bicycles?

65% of students in a class have got a bicycle.
This means that if there were 100 students, out of them 65 would have bicycles.
Therefore, students do not have got a bicycle
= (100 – 65)%
= 35%.

##### Question 21:

We have a basket full of apples, oranges and mangoes. If 50% are apples, 30% are oranges then what per cent are mangoes?

This means that if there are 100 given fruit items in the basket then numbers are 50 apples, 30 oranges and remaining mangoes.
Therefore, per cent of mangoes
= (100 – 50 – 30)%
= 20%.

##### Question 22:

Yes ; such type of more examples are as follows:
(i) In a class VII, a test in Maths of 100 marks was conducted and observed that: 20% students got marks below 60. 38% students got marks between 60 and 75. 42% students got marks above 80.
(ii) An alloy is made of following compositions: 30% Copper 45% Nickel 25% Zinc. Similarly, other examples of such types can be thought.

##### Question 23:

What per cent of these figures are shaded?

Find 50% of 164.

Find 75% of 12.

##### Question 26:

Find 12½ % of 64.

##### Question 27:

8% children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain?

##### Question 28:

9 is 25% of what number?

##### Question 29:

75% of what number is 15?

##### Question 30:

Convert the given fractional numbers to per cents.

##### Question 31:

Convert the given fractional numbers to per cents.

##### Question 32:

Convert the given fractional numbers to per cents.

##### Question 33:

Convert the given fractional numbers to per cents.

##### Question 34:

Convert the given decimal fractions to per cents:
0. 65

##### Question 35:

Convert the given decimal fractions to per cents:
2.1

##### Question 36:

Convert the given decimal fractions to per cents:
0.02

##### Question 37:

Convert the given decimal fractions to per cents:
12.35

##### Question 38:

Estimate what part of the figure is coloured and hence find the per cent which is coloured.

Total parts = 4
Coloured parts = 1

##### Question 39:

Estimate what part of the figure is coloured and hence find the per cent which is coloured.

Total parts = 5
Coloured parts = 3

##### Question 40:

Estimate what part of the figure is coloured and hence find the per cent which is coloured.

Total parts = 8
Coloured parts = 3

Find:
15% of 250

Find:
1% of 1 hour

##### Question 43:

Find:
20% of ₹2500

Hence, 20% of₹2500 is ₹500.

Find:
75% of 1 kg

75% of 1 kg

##### Question 45:

Find the whole quantity if
5% of it is 600.

##### Question 46:

Find the whole quantity if
12% of it is ₹1080.

##### Question 47:

Find the whole quantity if
40% of it is 500 km.

##### Question 48:

Find the whole quantity if
70% of it is 14 minutes.

##### Question 49:

Find the whole quantity if
8% of it is 40 litres.

Hence, required whole quantity is 500 litres.

##### Question 50:

Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%

Given per cents are converted into decimal fractions and also to fractions in simplest forms as follows:

##### Question 51:

In a city, 30% are females, 40% are males and remaining are children. What per cent are children?

This means that if total population of city were 100, out of them 30 would be females and 40 males and remaining children.
Then children would obviously be
= (100 – 30 – 40)%
= (100 – 70)%
= 30%.

##### Question 52:

Out of 15,000 voters in a tage of voters constituency, 60% voted. Find the per centage of voters who did not vote. Can you now find how many actually did not vote?

60% voted ; means if there were 100 voters, out of them 60 voted and remaining did not vote.
Then voters who did not vote = (100 – 60)% = 40%
Now, actual number of voters who did not vote

##### Question 53:

Meeta saves ₹400 from her salary. If this is 10% of her salary. What is her salary?

Let salary of Meeta = ₹P
∴Saving from her salary is 10% of P.
Actual saving = ₹400
Now, 10% of P = ₹400

##### Question 54:

A Local Cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Out of 100 matches number of matches won = 25
Out of 20 matches number of matches won =

##### Question 55:

Divide 15 sweets between Manu and Sonu so that they get 20% and 80% of them respectively.

##### Question 56:

If angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle.

Let actual angles of a triangle be 2x, 3x and 4x where x is constant and x > 0.
We know that
Sum of angles of triangle = 180°

##### Question 57:

Find percentage increase or decrease:
Price of a shirt decreased from ₹80 to ₹60.

Decreased price of shirt =₹(80 – 60)
= ₹20

##### Question 58:

Find percentage increase or decrease:
Marks in a test increased from 20 to 30.

Increased marks = 30 – 20
= 10

##### Question 59:

My mother says, in her childhood petrol was ₹1 a litre. It is ₹52 per litre today. By what percentage has the price gone up?

##### Question 60:

A shopkeeper bought a chair for ₹375 and sold it for ₹400. Find the percentage gain.

CP of a chair =₹375

##### Question 61:

Cost of an item is₹50. It was sold with a profit of 12%. Find the selling price.

##### Question 62:

An article was sold for ₹250 with a profit of 5%. What was its cost price?

##### Question 63:

An item was sold for₹540 at a loss of 5%. What was its cost price?

##### Question 64:

₹10,000 is invested at 5% interest rate p.a. Find the interest at the end of one year.

##### Question 65:

₹3,500 is given at 7% p.a. rate of interest. Find the interest which will be received at end of two years.

Principal; P =₹3,500

##### Question 66:

₹6,050 is borrowed at 6.5% rate of interest p.a. Find the interest and amount to be paid at the end of 3 years.

##### Question 67:

₹7,000 is borrowed at 3.5% rate of interest p.a. borrowed for 2 years. Find the amount to be paid at the end of the second year.

##### Question 68:

You have ₹2400 in your account and the interest rate is 5%. After how many years would you earn₹240 as interest.

##### Question 69:

On a certain sum the interest paid after 3 years is₹450 at 5% rate of interest per annum. Find the sum.

##### Question 70:

Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
Gardening shears bought for ₹250 and sold for ₹325.

CP of gardening shears = ₹250
SP of gardening shears = ₹325
SP is more than CP.

##### Question 71:

Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
A refrigerator bought for ₹12,000 and sold at ₹13,500.

CP of refrigerator = ₹12,000
SP of refrigerator = ₹13,500

##### Question 72:

Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
A cupboard bought for ₹2500 and sold at ₹3000.

##### Question 73:

Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
A skirt bought for₹250 and sold at ₹150.

CP of a skirt = ₹250
SP of a skirt = ₹150

##### Question 74:

Convert each part of the ratio to percentage:
3 : 1

Given ratio = 3 : 1

##### Question 75:

Convert each part of the ratio to percentage:
2 : 3 : 5

Given ratio = 2 : 3 : 5

##### Question 76:

Convert each part of the ratio to percentage:
1 : 4

Given ratio = 1 : 4

##### Question 77:

Convert each part of the ratio to percentage:
1 : 2 : 5

Given ratio = 1 : 2 : 5

##### Question 78:

The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.

##### Question 79:

Arun bought a car for ₹3,50,000. The next year, the price went upto ₹3,70,000. What was the percentage of price increase?

##### Question 80:

I buy a T.V. for ₹10,000 and sell it at a profit of 20%. How much money do I get for it?

CP of T.V. = ₹10,000

##### Question 81:

Juhi sells a washing machine for₹13,500. She loses 20% in the bargain. What was the price at which she bought it?

Hence, Juhi bought washing machine at ₹16875.

##### Question 82:

Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find percentage of carbon in chalk.

Given ratio = 10 : 3 : 12
Total of parts = 10 + 3 + 12
= 25

##### Question 83:

Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?

##### Question 84:

Amina buys a book for₹275 and sells it at a loss of 15%. How much does she sell it for?

##### Question 85:

Find the amount to be paid at end of 3 years in each case:
Principal = ₹12,00 at 12% p.a.

##### Question 86:

Find the amount to be paid at end of 3 years in each case:
Principal = ₹7,500 at 5% p.a.