A student was asked to multiply a number by `(3)/(2)` but he divided that number by `(3)/(2)`. His result was 10 less than the correct answer. The number was:

Options

A. 10
B. 12
C. 15
D. 20

Answer

Let's solve the problem step by step.

### Step 1: Define the variable
Let the number be \( x \).

### Step 2: Write the correct operation
The student was supposed to multiply the number by \( \frac{3}{2} \). Therefore, the correct answer would be:
\[ \text{Correct Answer} = x \times \frac{3}{2} = \frac{3x}{2} \]

### Step 3: Write the incorrect operation
Instead, the student divided the number by \( \frac{3}{2} \). The result of this operation would be:
\[ \text{Incorrect Answer} = x \div \frac{3}{2} = x \times \frac{2}{3} = \frac{2x}{3} \]

### Step 4: Set up the equation
According to the problem, the incorrect answer was 10 less than the correct answer. We can set up the equation:
\[ \frac{2x}{3} = \frac{3x}{2} - 10 \]

### Step 5: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by 6 (the least common multiple of the denominators 3 and 2):
\[ 6 \times \frac{2x}{3} = 6 \times \left(\frac{3x}{2} - 10\right) \]
This simplifies to:
\[ 4x = 9x - 60 \]

### Step 6: Solve for \( x \)
Now, we can rearrange the equation to solve for \( x \):
\[ 4x - 9x = -60 \]
\[ -5x = -60 \]
Dividing both sides by -5 gives:
\[ x = 12 \]

### Conclusion
The number is \( 12 \).

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