An amount of Rs. 380 is to be divided among 5 men, 8 boys and 4 women such that the ratio of amount received by the three is in the ratio of `8:4:7`. What Is the share of a woman?

Options

A. Rs 35
B. Rs 36.5
C. Rs 40
D. Rs 32.8

Answer

To solve the problem of dividing Rs. 380 among 5 men, 8 boys, and 4 women in the ratio of 8:4:7, we will follow these steps:

### Step 1: Understand the Ratio
The ratio of the amounts received by men, boys, and women is given as 8:4:7. This means:
- For every 8 parts received by men,
- 4 parts received by boys,
- 7 parts received by women.

### Step 2: Calculate the Total Parts in the Ratio
To find the total number of parts in the ratio, we add the parts together:
\[ 8 + 4 + 7 = 19 \text{ parts} \]

### Step 3: Determine the Value of One Part
Next, we need to find the value of one part by dividing the total amount (Rs. 380) by the total number of parts (19):
\[ \text{Value of one part} = \frac{380}{19} = 20 \text{ Rs.} \]

### Step 4: Calculate the Share of Women
Since the ratio for women is 7 parts, we can find the total amount received by the 4 women:
\[ \text{Total amount for women} = 7 \times 20 = 140 \text{ Rs.} \]

### Step 5: Calculate the Share of One Woman
To find the share of one woman, we divide the total amount for women by the number of women (4):
\[ \text{Share of one woman} = \frac{140}{4} = 35 \text{ Rs.} \]

### Final Answer
The share of one woman is Rs. 35.

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