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# (i) In a mixture of 45 litres, the ratio of milk to water is 13: 2. How much water must be added to this mixture to make the ratio of milk to water as 3: 1? (ii) The ratio of the number of boys to the numbers of girls in a school of 560 pupils is 5: 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3: 2.

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Question no.19 From ML aggarwal book, class10, chapter 7, ratio and proportion

In first question we have been given the ratio of milk and water in mixture amd after adding water ratio gets changed so we have to find the quantity of water being added.

In second question ratio of girl and boy is given after adding boys and girls in distinct numbers ratio of them changes. So we havr to find the no of girls that can be added to meet the required ratio.

Ques no. 19

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1. Solution:

(i) It is given that

Mixture of milk to water = 45 litres

Ratio of milk to water = 13: 2

Sum of ratio = 13 + 2 = 15

Here the quantity of milk = (45 × 13)/ 15 = 39 litres

Quantity of water = 45 × 2/15 = 6 litres

Consider x litre of water to be added, then water = (6 + x) litres

Here the new ratio = 3: 1

39: (6 + x) = 3: 1

We can write it as

39/ (6 + x) = 3/1

By cross multiplication

39 = 18 + 3x

3x = 39 – 18 = 21

x = 21/3 = 7 litres

Hence, 7 litres of water is to be added to the mixture.

(ii) It is given that

Ratio between boys and girls = 5: 3

Number of pupils = 560

So the sum of ratios = 5 + 3 = 8

We know that

Number of boys = 5/8 × 560 = 350

Number of girls = 3/8 × 560 = 210

Number of new boys admitted = 10

So the total number of boys = 350 + 10 = 360

Consider x as the number of girls admitted

Total number of girls = 210 + x

Based on the condition

360: 210 + x = 3: 2

We can write it as

360/ 210 + x = 3/2

By cross multiplication

630 + 3x = 720

3x = 720 – 630 = 90

So we get

x = 90/3 = 30

Hence, 30 new girls are to be admitted.

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