# NCERT Solutions For Class 6 Maths Chapter 12 Exercise 12.2

## Ncert Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2:-

**Exercise 12.2**Class 6 maths NCERT solutions Chapter 12 Ratio And Proportion pdf download:-

### Ncert Solution for Class 6 Maths Chapter 11 Ratio And Proportion Exercise 12.2 Tips:-

**Proportion**

Consider this situation :

Raju went to the market to purchase tomatoes. One shopkeeper tells him

that the cost of tomatoes is ` 40 for 5 kg. Another shopkeeper gives the cost as 6

kg for ` 42. Now, what should Raju do? Should he purchase tomatoes from the

first shopkeeper or from the second? Will the comparison by taking the difference

help him decide? No. Why not?

Think of some way to help him. Discuss it with your friends.

Consider another example.

Bhavika has 28 marbles and Vini has 180 flowers. They want to share

these among themselves. Bhavika gave 14 marbles to Vini and Vini gave 90

The breadth of the hall 10 40

The length of the hall 25 50

flowers to Bhavika. But Vini was not satisfied.

She felt that she had given more flowers to

Bhavika than the marbles given by Bhavika

to her.

What do you think? Is Vini correct?

To solve this problem both went to Vini’s

mother Pooja.

Pooja explained that out of 28 marbles,

Bhavika gave 14 marbles to Vini.

Therefore, ratio is 14 : 28 = 1 : 2.

And out of 180 flowers, Vini had given 90 flowers to Bhavika.

Therefore, ratio is 90 : 180 = 1 : 2.

Since both the ratios are the same, so the distribution is fair.

Two friends Ashma and Pankhuri went to the market to purchase hair clips.

They purchased 20 hair clips for 30. Asthma gave 12 and Pankhuri gave ` 18.

After they came back home, Ashma asked Pankhuri to give 10 hair clips to her.

But Pankhuri said, “since I have given more money so I should get more clips.

You should get 8 hair clips and I should get 12”.

Can you tell who is correct, Ashma or Pankhuri? Why?

The ratio of money given by Ashma to the money given by Pankhuri

= ` 12 : ` 18 = 2 : 3

According to Ashma’s suggestion, the ratio of the number of hair clips for

Ashma to the number of hair clips for Pankhuri = 10 : 10 = 1 : 1

According to Pankhuri’s suggestion, the ratio of the number of hair clips

for Ashma to the number of hair clips for Pankhuri = 8: 12 = 2 : 3

Now, notice that according to Ashma’s distribution, the ratio of hair clips and

the ratio of money given by them is not the same. But according to the

Pankhuri’s distribution of the two ratios is the same.

Hence, we can say that Pankhuri’s distribution is correct.

Sharing a ratio means something!

Consider the following examples :

Raj purchased 3 pens for ` 15 and Anu purchased 10 pens for ` 50. Whose

pens are more expensive?

The ratio of number of pens purchased by Raj to the number of pens purchased

by Anu = 3:10.

Ratio of their costs = 15 : 50 = 3 : 10

Both ratios 3: 10 and 15: 50 are equal. Therefore, the pens were

purchased for the same price by both.

Rahim sells 2 kg of apples for ` 60 and Roshan sells 4 kg of apples for

` 120. Whose apples are more expensive?

Ratio of the weight of apples = 2 kg : 4 kg = 1 : 2

Ratio of their cost = ` 60 : ` 120 = 6 : 12 = 1 : 2

So, the ratio of the weight of apples = ratio of their cost.

Since both the ratios are equal, hence, we say that they

are in proportion. They are selling apples at the same rate.

If two ratios are equal, we say that they are in proportion and use the

the symbol ‘::’ or ‘=’ to equate the two ratios.

For the first example, we can say 3, 10, 15 and 50 are in

the proportion which is written as 3:10::15:50 and is read as

3 is to 10 as 15 is to 50 or it is written as 3:10 = 15: 50.

For the second example, we can say 2, 4, 60 and 120 are

in the proportion which is written as 2:4:: 60:120 and is read

as 2 is to 4 as 60 is to 120.

Let us consider another example.

A man travels 35 km in 2 hours. With the same speed would

he is able to travel 70 km in 4 hours?

Now, the ratio of the two distances travelled by the man is 35 to

70 = 1:2 and the ratio of the time taken to cover these distances is 2 to 4 = 1:2

Hence, the two ratios are equal i.e. 35:70 = 2:4.

Therefore, we can say that the four numbers

35, 70, 2 and 4 are in proportion.

Hence, we can write it as 35:70::2:4 and

read it as 35 is to 70 as

2 is to 4. Hence, he can travel 70 km in 4

hours with that speed.

Now, consider this example.

Cost of 2 kg of apples is ` 60 and a 5 kg

watermelon costs ` 15.

Now, the ratio of the weight of apples to the

weight of watermelon is 2:5.

And the ratio of the cost of apples to the cost

of the watermelon is 60:15 = 4:1.

Here, the two ratios 2:5 and 60:15 are not equal,

i.e. 2 : 5 ≠ 60 : 15

Therefore, the four quantities 2, 5, 60 and 15 are not in proportion.

Check whether the given

ratios are equal, i.e. they are

in proportion.

If yes, then write them in

the proper form.

1. 1:5and 3:15

2. 2:9 and 18:81

3. 15:45 and 5:25

4. 4:12 and 9:27

5. 10 to 15 and 4 to 6