Question

Read the following passage:

A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹9,000 and from batch II is ₹26,000. Assume that each poor child pays ₹x per month and each rich child pays ₹y per month.

Based on the above information, answer the following questions:

1. Represent the information given above in terms of x and y.
2. Find the monthly fee paid by a poor child.
   OR
   Find the difference in the monthly fee paid by a poor child and a rich child.
3. If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?

Answer 1

i. Since, each poor child pays ₹ x

and each rich child pays ₹ y

∴ In batch I, 20 poor and 5 rich children pays ₹ 9000 can be represented as 20x + 5y = 9000

and In batch II, 5 poor and 25 rich children pays ₹ 26,000 can be represented as 5x + 25y = 26,000

ii. As we have 20x + 5y = 9,000        ...(1)

and 5x + 25y = 26,000

or x + 5y = 5,200           ...(2)

On subtracting (2) from (1), we get

19x = 3,800

`\implies` x = 200

∴ Monthly fee paid by a poor child = ₹ 200

OR

As we have,

20x + 5y = 9000       ...(i)

and 5x + 25y = 26000

x + 5y = 5200         ...(ii)

On subtracting equation (ii) from (i), we have

19x = 3800

x = `3800/19`

= 200

Put the value of x in equation (ii), we get

200 + 5y = 5200

5y = 5200 – 200

y = 1000

∴ y – x = 1000 – 200

= 800

Hence, difference in the monthly fee paid by a poor child and a rich child is ₹ 800.

iii. Total monthly fee = 10x + 20y

= 10(200) + 20(1,000)

= 2,000 + 20,000

= ₹ 22,000