A group collects as many paise from each member as the number of members in the group. If the total collection is ₹ 22.09 (i.e., 2209 paise), how many members are there in the group?

Introduction / Context: This is a classic squares problem. If each of n members contributes n paise, the total is n * n = n^2 paise. The question gives the total in rupees, which must be converted to paise first.

Given Data / Assumptions:

• Total collection = ₹ 22.09 = 2209 paise.
• Each member contributes an amount in paise equal to the number of members.

Concept / Approach: Total paise collected equals n^2. Therefore, n = √(total paise). Compute the integer square root of 2209.

Step-by-Step Solution: Convert to paise: ₹ 22.09 = 22 * 100 + 9 = 2209 paise. Let number of members be n. Total = n^2 paise ⇒ n = √2209. 2209 = 47^2 (since 47 * 47 = 2209). Hence, n = 47.

Verification / Alternative check: If there are 47 members and each pays 47 paise, total = 47 * 47 = 2209 paise = ₹ 22.09, consistent with the given total.

Why Other Options Are Wrong: 37^2 = 1369, 43^2 = 1849, 107^2 = 11449; none match 2209.

Common Pitfalls: Forgetting to convert rupees to paise or assuming the contribution is in rupees rather than paise.

Final Answer: 47