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 :

Question

Accepted Answer

To solve the problem and justify why Option 1 is correct, let's break down the situation:

1. **Understanding the Problem:**
   - The student was supposed to multiply a number by 25.
   - Instead, he multiplied the number by 52.
   - The result he got was 324 more than the correct answer.

2. **Setting Up the Equation:**
   - Let the number be $ x $.
   - The correct multiplication would be $ 25x $.
   - The incorrect multiplication was $ 52x $.
   - According to the problem, $ 52x = 25x + 324 $.

3. **Solving the Equation:**
   - Subtract $ 25x $ from both sides: $ 52x - 25x = 324 $.
   - Simplify: $ 27x = 324 $.
   - Divide both sides by 27 to solve for $ x $: $ x = \frac{324}{27} $.
   - Calculate: $ x = 12 $.

4. **Conclusion:**
   - The number to be multiplied was 12, which corresponds to Option 1.

5. **Explanation for Other Options:**
   - **Option 2 (15):** If $ x = 15 $, then $ 52 \times 15 = 780 $ and $ 25 \times 15 = 375 $. The difference is $ 780 - 375 = 405 $, not 324.
   - **Option 3 (25):** If $ x = 25 $, then $ 52 \times 25 = 1300 $ and $ 25 \times 25 = 625 $. The difference is $ 1300 - 625 = 675 $, not 324.
   - **Option 4 (32):** If $ x = 32 $, then $ 52 \times 32 = 1664 $ and $ 25 \times 32 = 800 $. The difference is $ 1664 - 800 = 864 $, not 324.

By following the logical steps and calculations, we confirm that Option 1 is indeed the correct answer, as it satisfies the condition given in the problem.