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# (i) The monthly pocket money of Ravi and Sanjeev are in the ratio 5: 7. Their expenditures are in the ratio 3: 5. If each saves Rs 80 per month, find their monthly pocket money. (ii) In class X of a school, the ratio of the number of boys to that of the girls is 4: 3. If there were 20 more boys and 12 less girls, then the ratio would have been 2: 1. How many students were there in the class?

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Question no.20  From ML aggarwal book, class10, chapter 7, ratio and proportion

In the first question we have been given ratio of pocket money of two persons also ratio of their expenditures and the amount of saving they each save. And we are asked finally the monthly pocket money.

Im second ques ratio of boys to girls is given. Their ratio get changes if we change the number of boys and girls according to question. We have to. Find the total no of students

Question 20

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1. Solution:

(i) Consider the monthly pocket money of Ravi and Sanjeev as 5x and 7x

Their expenditure is 3y and 5y respectively.

5x – 3y = 80 …… (1)

7x – 5y = 80 …… (2)

Now multiply equation (1) by 7 and (2) by 5

Subtracting both the equations

35x – 21y = 560

35x – 25y = 400

So we get

4y = 160

y = 40

In equation (1)

5x = 80 + 3 × 40 = 200

x = 40

Here the monthly pocket money of Ravi = 5 × 40 = 200

(ii) Consider x as the number of students in class

Ratio of boys and girls = 4: 3

Number of boys = 4x/7

Number of girls = 3x/7

Based on the problem

(4x/7 + 20): (3x/7 – 12) = 2: 1

We can write it as

(4x + 140)/ 7: (3x – 84)/ 7 = 2: 1

So we get

(4x + 140)/ 7 × 7/ (3x – 84) = 2/1

(4x + 140)/ (3x – 84) = 2/1

6x – 168 = 4x + 140

6x – 4x = 140 + 168

2x = 308

x = 308/2 = 154

Therefore, 154 students were there in the class.

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