A boy was asked to find the value of `(3)/(8)` of a sum of money. Instead of multiplying the sum by `(3)/(8)` he divided it by `(3)/(8)` and then his answer exceeded by 55. Find the correct answer?

Options

A. Rs 9
B. Rs 24
C. Rs 64
D. Rs 1,320

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let the sum of money be represented by \( x \).

### Step 2: Calculate the Correct Value
The boy was supposed to find \( \frac{3}{8} \) of the sum of money. This can be calculated as:
\[ \text{Correct Value} = \frac{3}{8} x \]

### Step 3: Calculate the Incorrect Value
Instead of multiplying, the boy divided the sum by \( \frac{3}{8} \). Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \text{Incorrect Value} = x \div \frac{3}{8} = x \times \frac{8}{3} = \frac{8}{3} x \]

### Step 4: Set Up the Equation
According to the problem, the incorrect value exceeded the correct value by 55:
\[ \frac{8}{3} x - \frac{3}{8} x = 55 \]

### Step 5: Find a Common Denominator
To solve the equation, we need a common denominator. The least common multiple of 3 and 8 is 24. We can rewrite the fractions:
\[ \frac{8}{3} x = \frac{64}{24} x \quad \text{and} \quad \frac{3}{8} x = \frac{9}{24} x \]

### Step 6: Substitute Back into the Equation
Now substituting back into the equation, we have:
\[ \frac{64}{24} x - \frac{9}{24} x = 55 \]

### Step 7: Combine Like Terms
Combine the fractions:
\[ \frac{64 - 9}{24} x = 55 \]
\[ \frac{55}{24} x = 55 \]

### Step 8: Solve for \( x \)
To isolate \( x \), multiply both sides by 24:
\[ 55x = 55 \times 24 \]
\[ x = 24 \]

### Step 9: Calculate the Correct Value
Now, we can find the correct value:
\[ \text{Correct Value} = \frac{3}{8} \times 24 = 9 \]

### Final Answer
The correct answer is \( 9 \).

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