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 ₹ 9000 and from batch II is ₹ 26,000. Assume that each poor child pays ₹ x per month and each rich child pays ₹ y per month.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding stimulus
Model Answer
(i) From the given information:
- Batch I: $20x + 5y = 9000$
- Batch II: $5x + 25y = 26000$
(ii) From the two equations:
$20x + 5y = 9000$ … (1)
$5x + 25y = 26000$ … (2)
Multiply (1) by 5: $100x + 25y = 45000$ … (3)
Subtract (2) from (3):
$95x = 19000$
$x = 200$
∴ Monthly fee paid by a poor child = ₹ 200
(iii) From (2), substituting $x = 200$:
$5(200) + 25y = 26000 \Rightarrow 25y = 25000 \Rightarrow y = 1000$
For 10 poor and 20 rich children in batch II:
Total = $10x + 20y = 10(200) + 20(1000) = 2000 + 20000 =$ ₹ 22,000
Source: Pair of Linear Equations in Two Variables, Case Study Application
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Explanation
- (i) Simply translate the word problem into two linear equations — 1 mark for both equations correct.
- (ii) Solve by elimination (multiply and subtract). Show all steps for full 2 marks; a missing step costs a mark.
- (iii) You must first find $y$ (₹ 1000) using the value of $x$, then substitute the new batch composition. Just the final answer without working may lose the mark.