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

Introduction / Context:
This question is about forming an equation from a word problem involving rupees and paise. Each member of a club contributes an amount that depends on the number of members, and the total contribution is given. Using the relationship between rupees, paise and the number of members, we must find the total membership of the club.

Given Data / Assumptions:
- Let the number of members in the club be n.
- Each member contributes n rupees and n paise.
- One rupee equals 100 paise.
- Total contribution by all members together is Rs 2525.
- We need to determine the value of n, the number of members.

Concept / Approach:
We first express the contribution of one member in rupees by converting paise to rupees. Then we multiply this amount by the number of members to get the total contribution. This total is equated to 2525, giving an equation in terms of n. Solving the equation yields the number of members. The algebra involves a simple quadratic that turns out to be a perfect square, making it easy to solve.

Step-by-Step Solution:
Step 1: Each member contributes n rupees and n paise.Step 2: Convert n paise to rupees. This is n / 100 rupees.Step 3: Contribution of each member in rupees = n + n / 100 = n * (1 + 1 / 100) = n * 101 / 100.Step 4: Since there are n members, total contribution = n * (n * 101 / 100) = n^2 * 101 / 100.Step 5: We are told that this total equals 2525, so n^2 * 101 / 100 = 2525.Step 6: Multiply both sides by 100 to remove the denominator: n^2 * 101 = 2525 * 100.Step 7: Compute the right side: 2525 * 100 = 252500.Step 8: Now n^2 = 252500 / 101. Since 2525 = 101 * 25, we get 252500 / 101 = 2500.Step 9: Thus n^2 = 2500, so n = 50 (number of members must be positive).

Verification / Alternative check:
If there are 50 members, each member contributes 50 rupees and 50 paise. Fifty paise is 0.50 rupees, so each member pays Rs 50.50. Total contribution = 50 * 50.50 = 2525 rupees, which matches the amount stated in the problem. Therefore, the calculation is fully consistent.

Why Other Options Are Wrong:
If n were 45, 55 or 60, then n^2 * 101 / 100 would not equal 2525. For example, if n = 60, total contribution would be 60^2 * 101 / 100 = 3600 * 101 / 100 = 3636, which is far greater than 2525. Similar mismatches occur with the other incorrect options.

Common Pitfalls:
Students sometimes forget to convert paise to rupees correctly, or they simply multiply n rupees and n paise without combining them into a single rupee value. Others assume that total contribution is proportional to n rather than n squared. Always express each member contribution clearly, convert units properly and only then multiply by the number of members.

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