Each member of a club contributes as many rupees and as many paise as the total number of members in the club. If the total contribution collected from all members is Rs 2525, how many members are there in the club?

Introduction / Context:
This question involves understanding money in rupees and paise and setting up a quadratic equation. Each member contributes an amount that depends on the total number of members, and you are asked to find that number given the total contribution.

Given Data / Assumptions:
• Let the number of members in the club be n.• Each member contributes n rupees and n paise.• Total contribution from all members is Rs 2525.• We use 100 paise = 1 rupee.

Concept / Approach:
If there are n members, and each gives n rupees and n paise, then each member contributes n + n/100 rupees. The total contribution is n times this amount. This leads to a quadratic equation in n, which we solve to find the number of members. We also check that the solution is a positive integer that makes sense in the context of the problem.

Step-by-Step Solution:
Step 1: Let the number of members be n.Step 2: Each member contributes n rupees and n paise.Step 3: Convert n paise to rupees: n paise = n / 100 rupees.Step 4: So contribution per member in rupees = n + n / 100 = (100n + n) / 100 = 101n / 100.Step 5: Total contribution from n members = n * (101n / 100) rupees.Step 6: Given total contribution = Rs 2525, so n * (101n / 100) = 2525.Step 7: Multiply both sides by 100: 101n^2 = 2525 * 100 = 252500.Step 8: Divide both sides by 101: n^2 = 252500 / 101.Step 9: Note that 101 * 2500 = 252500, so n^2 = 2500.Step 10: Therefore, n = square root of 2500 = 50 (reject negative value).

Verification / Alternative check:
If n = 50, then each member contributes 50 rupees and 50 paise. In rupees, that is 50.50 or 50 + 50 / 100. Total contribution = 50 * 50.50 = 50 * 50.5 = 2525, which matches the given total. This confirms that n = 50 is correct.

Why Other Options Are Wrong:
60, 45, 55: Substituting these values into the expression n * (101n / 100) does not yield 2525. The resulting totals differ from the given amount, so these cannot be the correct number of members.

Common Pitfalls:
Some students forget to convert paise into rupees or misinterpret the phrase as n rupees or n paise instead of both. Others may make algebraic mistakes when forming or solving the quadratic equation. Careful unit conversion and stepwise algebra help avoid errors.

Final Answer:
The number of members in the club is 50.