Rs. 4536 is divided among 4 men, 5 women and 2 boys. The ratio of shares of a man, a woman and a boy is 7 : 4 : 3. The share of a woman is :

Question

Accepted Answer

To determine the share of a woman, we need to first understand the distribution of Rs. 4536 among 4 men, 5 women, and 2 boys based on the given ratio of their shares, which is 7:4:3 for a man, a woman, and a boy, respectively.

1. **Calculate the total parts in the ratio:**
   - For 1 man, the share is 7 parts.
   - For 1 woman, the share is 4 parts.
   - For 1 boy, the share is 3 parts.

Therefore, the total parts for all individuals are:
   - Total parts for men = 4 men × 7 parts = 28 parts
   - Total parts for women = 5 women × 4 parts = 20 parts
   - Total parts for boys = 2 boys × 3 parts = 6 parts

Total parts = 28 + 20 + 6 = 54 parts

2. **Calculate the value of one part:**
   - Total amount = Rs. 4536
   - Value of one part = Total amount / Total parts = Rs. 4536 / 54 = Rs. 84

3. **Calculate the share of a woman:**
   - Share of one woman = 4 parts
   - Therefore, the share of one woman = 4 parts × Rs. 84 per part = Rs. 336

Thus, the share of a woman is Rs. 336, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

- **Option 1 (Rs. 324):** This amount does not match the calculated share of a woman, which is Rs. 336. It is not consistent with the value derived from the given ratio and total amount.

- **Option 2 (Rs. 168):** This amount is significantly lower than the calculated share of Rs. 336. It does not align with the distribution based on the ratio 7:4:3.

- **Option 3 (Rs. 224):** This amount is also less than the calculated share of Rs. 336. It does not fit the correct distribution of the total amount among the individuals.

Therefore, Option 4 (Rs. 336) is the correct answer, as it accurately reflects the share of a woman based on the given ratio and total amount.