Understanding the Club Contribution Problem

This problem involves a club where each member contributes a specific amount related to the total number of members. We are given the total contribution and need to find the number of members.

Let's break down the problem:

• Let 'n' be the number of members in the club.
• Each member contributes 'n' rupees and 'n' paise.
• The total contribution is Rs. 2525.

Setting Up the Equation for Total Contribution

The contribution of one member is 'n' rupees and 'n' paise. To express this in rupees, we convert the paise to rupees:

1 rupee = 100 paise

So, 'n' paise is equal to \(\frac{n}{100}\) rupees.

The total contribution by one member in rupees is \(n + \frac{n}{100}\).

Since there are 'n' members, the total contribution by all members is the number of members multiplied by the contribution of one member:

Total Contribution = Number of Members \(\times\) Contribution per Member

Total Contribution \(= n \times \left(n + \frac{n}{100}\right)\)

We are given that the total contribution is Rs. 2525. So, we can write the equation:

\(n \times \left(n + \frac{n}{100}\right) = 2525\)

Solving for the Number of Members

Now, let's solve the equation for 'n':

First, simplify the expression inside the parenthesis:

\(n + \frac{n}{100} = \frac{100n}{100} + \frac{n}{100} = \frac{100n + n}{100} = \frac{101n}{100}\)

Substitute this back into the equation:

\(n \times \left(\frac{101n}{100}\right) = 2525\)

\(\frac{101n^2}{100} = 2525\)

To isolate \(n^2\), multiply both sides by 100:

\(101n^2 = 2525 \times 100\)

\(101n^2 = 252500\)

Now, divide both sides by 101:

\(n^2 = \frac{252500}{101}\)

Let's perform the division:

\(252500 \div 101 = 2500\)

\(n^2 = 2500\)

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

\(n = \sqrt{2500}\)

\(n = 50\)

Since 'n' represents the number of members, it must be a positive whole number. The value \(n=50\) is a valid solution.

Verifying the Answer

Let's check if 50 members results in a total contribution of Rs. 2525.

Number of members = 50

Contribution per member = 50 rupees and 50 paise

Contribution per member in rupees = \(50 + \frac{50}{100} = 50 + 0.50 = 50.50\) rupees

Total contribution = Number of members \(\times\) Contribution per member

Total contribution = \(50 \times 50.50\)

\(50 \times 50.50 = 50 \times \left(50 + \frac{1}{2}\right) = 50 \times 50 + 50 \times \frac{1}{2} = 2500 + 25 = 2525\)

The total contribution is indeed Rs. 2525, which matches the given information.

Comparing with Options

We found that the number of members is 50. Let's look at the given options:

• 60
• 45
• 55
• 50

Our calculated number of members, 50, matches one of the options.

Revision Table: Key Concepts

Additional Information: Related Problems

Problems involving contributions based on the number of participants are common in competitive exams. They often require setting up and solving quadratic equations or sometimes linear equations, depending on how the contribution is defined.

Key steps to solve such problems:

• Clearly identify the unknown quantity (e.g., number of members, amount contributed).
• Define a variable for the unknown.
• Express the contribution of one person and the total contribution in terms of the variable.
• Set up an equation using the given total amount.
• Solve the equation. Remember to consider only realistic solutions (e.g., positive integers for the number of people).

Understanding how to convert between different currency units (like rupees and paise, dollars and cents) is also crucial in such problems.