A student was asked to multiply a certain number by 3/8 but he divided the number by 3/8 . In this process he 8 got the answer 55 more than the actual answer. The actual answer is:

Question

Accepted Answer

To solve this problem, let's break down the situation step by step:

1. **Understanding the Error**: The student was supposed to multiply a number by $ \frac{3}{8} $, but instead, he divided the number by $ \frac{3}{8} $. This means the student performed the operation $ \text{Number} \times \frac{8}{3} $ instead of $ \text{Number} \times \frac{3}{8} $.

2. **Difference in Results**: The result of dividing by $ \frac{3}{8} $ is 55 more than the result of multiplying by $ \frac{3}{8} $.

3. **Setting Up the Equation**: Let the original number be $ x $.

- The correct operation (multiplication) would give: $ x \times \frac{3}{8} $.
   - The incorrect operation (division) gives: $ x \times \frac{8}{3} $.

According to the problem, the incorrect result is 55 more than the correct result:

$$
   x \times \frac{8}{3} = x \times \frac{3}{8} + 55
   $$

4. **Solving the Equation**:

- Multiply both sides by 24 to eliminate the fractions:

$$
     24 \times \left(x \times \frac{8}{3}\right) = 24 \times \left(x \times \frac{3}{8} + 55\right)
     $$

- Simplify:

$$
     8x = 9x + 1320
     $$

- Rearrange to solve for $ x $:

$$
     8x - 9x = 1320
     $$

$$
     -x = 1320
     $$

$$
     x = -1320
     $$

- However, since we are looking for a positive number, let's re-evaluate the setup. The correct setup should be:

$$
     \frac{8}{3}x - \frac{3}{8}x = 55
     $$

- Find a common denominator and solve:

$$
     \frac{64x - 9x}{24} = 55
     $$

$$
     \frac{55x}{24} = 55
     $$

$$
     55x = 1320
     $$

$$
     x = 24
     $$

- Correcting the calculation, we find $ x = 24 $.

5. **Verification**: Let's verify the calculation:

- Correct operation: $ 24 \times \frac{3}{8} = 9 $.
   - Incorrect operation: $ 24 \times \frac{8}{3} = 64 $.
   - Difference: $ 64 - 9 = 55 $.

Thus, the actual answer is indeed 9, which corresponds to Option 3.

**Explanation of Incorrect Options**:

- **Option 1 (18)**: If the number were 18, the calculations would not satisfy the condition that the incorrect result is 55 more than the correct result.
- **Option 2 (24)**: This was the number we calculated, not the result of the multiplication.
- **Option 4 (27)**: Similarly, this does not satisfy the condition when plugged into the equation.

Therefore, Option 3 is the correct answer, as it satisfies all the conditions given in the problem.