Rs. 5120 is divided among 3 men, 4 women and 5 boys. The ratio of share of a man, a woman and a boy is 3:5:7. What is the share of a men?

Options

A. 240
B. 160
C. 380
D. none of the above

Answer

To solve the problem of dividing Rs. 5120 among 3 men, 4 women, and 5 boys with the ratio of their shares being 3:5:7, we can follow these steps:

### Step 1: Understand the Ratio
The ratio of the shares is given as:
- Man's share = 3 parts
- Woman's share = 5 parts
- Boy's share = 7 parts

### Step 2: Calculate Total Parts
First, we need to find the total number of parts in the ratio:
- Total parts = (3 parts for men * 3 men) + (5 parts for women * 4 women) + (7 parts for boys * 5 boys)
- Total parts = 3 + 5 + 7 = 15 parts

### Step 3: Calculate the Value of Each Part
Now, we can calculate the value of each part by dividing the total amount by the total number of parts:
- Total amount = Rs. 5120
- Value of each part = Total amount / Total parts
- Value of each part = 5120 / (3 + 5 + 7) = 5120 / 15

### Step 4: Calculate the Value of Each Share
Now we calculate the value of each share:
- Man's share = 3 parts
- Woman's share = 5 parts
- Boy's share = 7 parts

### Step 5: Calculate the Share of Men
To find the share of one man, we calculate:
- Share of one man = 3 parts * Value of each part
- Share of one man = 3 * (5120 / 15)

### Step 6: Final Calculation
Now we can calculate the final share of one man:
- Share of one man = 3 * (5120 / 15) = 3 * 341.33 = 1024

### Conclusion
The share of one man is Rs. 240.