A cloth merchant announces a 25 percent rebate on the price of cloth. Cloth normally costs Rs 32 per metre. If a customer wants to receive a total rebate of Rs 40, how many metres of cloth must be purchased?

Introduction / Context:
This question is a direct application of percentage discount to find quantity purchased. The merchant offers a flat rebate percentage on a per metre price. The customer wants a specified amount of money saved through the rebate, and we need to connect rebate per metre with total rebate to find the required number of metres.

Given Data / Assumptions:
Rebate rate = 25 percent. Price of cloth per metre before rebate = Rs 32. Total rebate desired by the customer = Rs 40. The rebate is applied uniformly on every metre purchased.

Concept / Approach:
Rebate per metre is calculated as percentage rebate multiplied by marked price per metre. Once rebate per metre is known, total rebate equals rebate per metre multiplied by number of metres purchased. Hence, number of metres equals total rebate divided by rebate per metre. This is a straightforward proportional relationship.

Step-by-Step Solution:
Marked price per metre = Rs 32. Rebate rate = 25 percent, which is 25/100. Rebate per metre = 25/100 * 32. Compute 25/100 * 32 = 8. So the customer saves Rs 8 on each metre of cloth. Total rebate required = Rs 40. Number of metres to be purchased = total rebate / rebate per metre. Number of metres = 40 / 8 = 5 metres.

Verification / Alternative check:
We can check the answer by reversing the reasoning. If the customer buys 5 metres, total original cost is 5 * 32 = 160. Rebate at 25 percent is 25/100 * 160 = 40. This matches the required rebate, so 5 metres is correct. Trying any other option quickly shows that the rebate would not equal exactly Rs 40.

Why Other Options Are Wrong:
If 6 metres are bought, total rebate would be 6 * 8 = 48. For 10 metres, rebate is 80. For 7 metres, rebate is 56. For 8 metres, rebate is 64. None of these equal the target rebate of 40. Only 5 metres give exactly Rs 40 as rebate.

Common Pitfalls:
One common mistake is to compute 25 percent of 40 instead of 25 percent of the price per metre. Another error is to try to directly adjust the final price rather than focusing on rebate per unit. Clear separation between unit rebate and total rebate helps avoid confusion.

Final Answer:
The customer must purchase 5 metres of cloth to receive a total rebate of Rs 40.