Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is

Options

A. 60
B. 45
C. 55
D. 50

Answer

To solve the problem step by step, let's denote the number of members in the club as \( X \).

### Step 1: Understand the Contributions
Each member contributes:
- \( X \) rupees
- \( X \) paise

### Step 2: Convert Paise to Rupees
Since there are 100 paise in a rupee, the contribution in rupees from the paise is:
\[ \text{Contribution in rupees from paise} = \frac{X \text{ paise}}{100} = \frac{X}{100} \text{ rupees} \]

### Step 3: Calculate Total Contribution
The total contribution from all members can be expressed as:
\[ \text{Total contribution} = \text{Contribution from rupees} + \text{Contribution from paise} \]
Substituting the values, we have:
\[ \text{Total contribution} = X \cdot X + X \cdot \frac{X}{100} = X^2 + \frac{X^2}{100} \]

### Step 4: Combine the Contributions
To combine these, we can find a common denominator:
\[ X^2 + \frac{X^2}{100} = \frac{100X^2}{100} + \frac{X^2}{100} = \frac{101X^2}{100} \]

### Step 5: Set Up the Equation
According to the problem, the total contribution is Rs. 2525. Thus, we can set up the equation:
\[ \frac{101X^2}{100} = 2525 \]

### Step 6: Solve for \( X^2 \)
To eliminate the fraction, multiply both sides by 100:
\[ 101X^2 = 2525 \times 100 \]
Calculating the right side:
\[ 2525 \times 100 = 252500 \]
So we have:
\[ 101X^2 = 252500 \]

### Step 7: Isolate \( X^2 \)
Now, divide both sides by 101:
\[ X^2 = \frac{252500}{101} \]
Calculating the division:
\[ X^2 = 2500 \]

### Step 8: Solve for \( X \)
Taking the square root of both sides:
\[ X = \sqrt{2500} = 50 \]

### Conclusion
Thus, the number of members in the club is \( \boxed{50} \).

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