When a amount was distributed equally among 12 boys. Each of them got Rs. 60 more than the amount received by each boy when the same amount was distributed equally to 20 boys. What is the amount?

Options

A. Rs. 1800
B. Rs. 1440
C. Rs. 1600
D. Data inadequate

Answer

To solve the problem, we will denote the total amount as \( A \).

1. **Distributing the Amount Among 12 Boys:**
When the amount \( A \) is distributed among 12 boys, each boy receives:
\[ \text{Amount per boy} = \frac{A}{12} \]

2. **Distributing the Amount Among 20 Boys:**
When the same amount \( A \) is distributed among 20 boys, each boy receives:
\[ \text{Amount per boy} = \frac{A}{20} \]

3. **Setting Up the Equation:**
According to the problem, the amount received by each boy when distributed among 12 boys is Rs. 60 more than the amount received when distributed among 20 boys. Therefore, we can set up the equation:
\[ \frac{A}{12} = \frac{A}{20} + 60 \]

4. **Clearing the Fractions:**
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of 12 and 20, which is 60:
\[ 60 \cdot \frac{A}{12} = 60 \cdot \left(\frac{A}{20} + 60\right) \]
Simplifying this gives:
\[ 5A = 3A + 3600 \]

5. **Solving for A:**
Now, we can isolate \( A \):
\[ 5A - 3A = 3600 \]
\[ 2A = 3600 \]
\[ A = \frac{3600}{2} = 1800 \]

6. **Conclusion:**
The total amount \( A \) is Rs. 1800.