Solving a Group Contribution Problem: Number of Members in a Group

Imagine a scenario where a group of students decides to collect paise from each member, the amount collected being equivalent to the number of members. This intriguing problem involves understanding the conversion between rupees and paise and applying mathematical concepts to derive the solution. Below, we explore this problem step-by-step.

Understanding the Problem

The group of students decides to collect as many paise from each member as the number of members. If the total collection amounts to Rs. 59.29, we need to find out the number of members in the group.

Step-by-Step Solution

Let the number of members in the group be denoted as n. According to the problem, each member contributes an amount in paise equal to the number of members, which is n paise. Therefore, the total contribution from all members can be expressed as:

Total contribution n x n n2 paise

We need to convert Rs. 59.29 to paise. Since 1 Rupee is equal to 100 paise, we can express the total amount in paise as:

59.29 Rs 59.29 x 100 5929 paise

Setting up the equation, we have:

n2 5929

To find n, we take the square root of both sides:

n √5929

Calculating the square root:

n 77

Therefore, the number of members in the group is 77.

Alternative Method of Solution

Another way to approach this problem is by considering the number of students in the group as x. Each student contributes an amount of money equal to the total number of students in the group. Therefore:

Total amount collected x x x2

We are given that the total amount collected was Rs 59.29, so we can write:

x2 59.29

Converting Rs 59.29 to paise:

x2 59.29 x 100 5929

Taking the square root of both sides:

x √5929

x ≈ 7.7

Since the number of students must be a whole number, we round 7.7 to the nearest integer:

x ≈ 8

Thus, there were 8 students in the group.

Additional Example

To further illustrate, let's consider a hypothetical group with 'x' members, each contributing 'y' rupees. If the total contribution is the product of the number of members and the amount contributed by each, we get:

total amount collected x y

Given that each student contributes as much money as there are students, we have:

y x

Substituting y x in the first equation, we get:

total amount collected x x x2

We know the total collection was Rs 59.29, so:

x2 59.29

Converting Rs 59.29 to paise:

x2 5929 paise