`Rs1104` is divided between 3 men, 4 women and 6 boys, so that the share of a man, a woman and a boy are in the proportion of 3 : 2 : 1. How much does each boy get?

Options

A. `Rs48`
B. `Rs64`
C. `Rs96`
D. Cannot be determined

Answer

To solve the problem of dividing Rs. 1104 among 3 men, 4 women, and 6 boys in the ratio of their shares (3:2:1), we can follow these steps:

### Step 1: Define the shares
Let the share of a man be represented as \(3k\), the share of a woman as \(2k\), and the share of a boy as \(k\).

### Step 2: Calculate total shares
Now, we need to calculate the total shares contributed by all the men, women, and boys:
- Total share from 3 men = \(3 \times 3k = 9k\)
- Total share from 4 women = \(4 \times 2k = 8k\)
- Total share from 6 boys = \(6 \times k = 6k\)

Now, we can add these shares together:
\[ \text{Total shares} = 9k + 8k + 6k = 23k \]

### Step 3: Set up the equation
Since the total amount of money to be divided is Rs. 1104, we can set up the equation:
\[ 23k = 1104 \]

### Step 4: Solve for \(k\)
To find the value of \(k\), we divide both sides of the equation by 23:
\[ k = \frac{1104}{23} \]
Calculating this gives:
\[ k = 48 \]

### Step 5: Find the share of each boy
Since the share of one boy is \(k\), we have:
\[ \text{Share of one boy} = k = 48 \]

Thus, each boy gets Rs. 48.

### Final Answer:
Each boy gets Rs. 48.

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