Question

A coaching institute of mathematics conducts classes in two batches I and II and the 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 ₹ 9000 and from batch II is ₹ 26000. Assume that each poor child pays ₹ x per month and each rich child pay ₹ y per month.

Based on the above information, answer the following questions.

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

Answer 1

i. Batch I: \[20x + 5y = 9000\] 

Batch II: \[5x + 25y = 26000\] 

ii. Dividing the first by 5 gives \[4x + y = 1800\] so \[y = 1800 - 4x\] 

Dividing the second by 5 gives \[x + 5y = 5200\] 

Substituting: \[x + 5(1800 - 4x) = 5200\]

\[\Rightarrow -19x = -3800\]

\[\Rightarrow x = 200\] 

\[y = 1800 - 800 = 1000\] 

Monthly fee of a poor child = ₹ 200. 

iii. Difference: \[1000 - 200 = ₹800\] 

iv. Collection from batch II:

\[10 \times 200 + 20 \times 1000\]

\[= 2000 + 20000\]

\[= ₹22000\]