A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was:

Options

A. 12
B. 15
C. 25
D. 32

Answer

To solve the problem, let's denote the number to be multiplied as \( x \).

1. **Set up the equations**:
- The correct answer when multiplying by 25 is \( 25x \).
- The incorrect answer when multiplying by 52 is \( 52x \).
- According to the problem, the incorrect answer is 324 more than the correct answer. Therefore, we can write the equation:
\[ 52x = 25x + 324 \]

2. **Simplify the equation**:
- To isolate \( x \), we first subtract \( 25x \) from both sides:
\[ 52x - 25x = 324 \]
- This simplifies to:
\[ 27x = 324 \]

3. **Solve for \( x \)**:
- Now, we divide both sides by 27 to find \( x \):
\[ x = \frac{324}{27} \]
- Calculating the division gives:
\[ x = 12 \]

4. **Conclusion**:
- The number to be multiplied is \( 12 \).