A boy, after giving away 80% of his pocket money to one companion and 6% of the remainder to another, has 47 paise left with him. How much pocket money did the boy have in the beginning ?

Options

A. Rs.2
B. Rs. 2.50
C. Rs. 5
D. Rs. 10

Answer

To find out how much pocket money the boy had initially, we can follow these steps:

### Step 1: Define the initial amount
Let the initial pocket money be \( x \) paise.

### Step 2: Calculate the amount given to the first companion
The boy gives away 80% of his pocket money to the first companion.
So, the amount given to the first companion is:
\[ 0.80x \]

### Step 3: Calculate the remaining amount after the first companion
After giving away 80% of his pocket money, the remaining amount is:
\[ x - 0.80x = 0.20x \]

### Step 4: Calculate the amount given to the second companion
The boy then gives 6% of the remaining amount to the second companion.
So, the amount given to the second companion is:
\[ 0.06 \times (0.20x) = 0.012x \]

### Step 5: Calculate the remaining amount after the second companion
After giving away 6% of the remainder, the remaining amount is:
\[ 0.20x - 0.012x = 0.188x \]

### Step 6: Set up the equation based on the remaining amount
According to the problem, the boy has 47 paise left. Therefore, we can set up the equation:
\[ 0.188x = 47 \]

### Step 7: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 0.188:
\[ x = \frac{47}{0.188} \]

Calculating this gives:
\[ x \approx 250 \text{ paise} \]

### Step 8: Convert paise to rupees
Since 1 rupee = 100 paise, we convert 250 paise to rupees:
\[ \text{Rupees} = \frac{250}{100} = 2.5 \text{ rupees} \]

### Conclusion
The boy had **2.5 rupees** in the beginning.

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