Twelve boys agreed to contribute Rs 750 each to an orphanage. Before paying, some boys dropped out and so the remaining boys each had to pay Rs 150 more than originally planned. How many boys dropped out of the contribution plan?

Introduction / Context:
This contribution problem is a classic example of how a fixed total amount, when divided among fewer people, increases the per-head share. The original plan is that 12 boys each pay Rs 750. Then some boys drop out, and the remaining boys have to pay Rs 150 more each to keep the total contribution the same. We must determine how many boys dropped out.

Given Data / Assumptions:

• Originally, there were 12 boys.
• Each boy was supposed to pay Rs 750.
• Some number of boys dropped out before paying.
• Each of the remaining boys then paid Rs 150 more, that is Rs 900 each.
• The total contribution amount remained the same as originally planned.
• We must find how many boys dropped out.

Concept / Approach:
First, compute the original total planned contribution. Then let the number of boys who actually paid be N. These N boys each pay Rs 900 (750 + 150), and the total amount must equal the original total. Equating these totals gives a simple equation in N. Finally, the number of boys who dropped out is 12 minus N.

Step-by-Step Solution:
Original number of boys = 12.Original planned contribution per boy = Rs 750.So, original total contribution = 12 * 750 = Rs 9000.After some boys dropped out, each remaining boy paid Rs 150 more, that is 750 + 150 = Rs 900.Let the number of boys who actually paid be N.Total contribution with N boys is N * 900.This total must equal the original total, so N * 900 = 9000.Therefore, N = 9000 / 900 = 10.Number of boys who dropped out = 12 - 10 = 2.

Verification / Alternative check:
We can check by plugging the numbers back. If 10 boys each pay Rs 900, total contribution = 10 * 900 = Rs 9000, which is exactly the same as the original planned total. The drop from 12 to 10 boys is 2 boys, confirming that 2 boys dropped out. The change in per-head contribution is indeed Rs 150, matching the question.

Why Other Options Are Wrong:
If 3 or more boys had dropped out, the remaining number of boys would be less than 10 and they would have to pay more than Rs 900 each to maintain the same total. Similarly, if only 1 boy had dropped out, 11 boys paying Rs 900 each would contribute Rs 9900, which is more than the original total. Options 4, 5 or 6 would yield even larger discrepancies. Only 2 boys dropped out fits the numbers correctly.

Common Pitfalls:
Some test takers forget that the total contribution does not change and treat Rs 900 as the new target total per boy without connecting it to the original Rs 9000. Others miscompute the original total or divide by the wrong amount when solving for N. Always compute the original total first, then use the new per-head amount to solve for the new number of contributors.

Final Answer:
The number of boys who dropped out is 2.