Rs.1040 is divided among 2 men, 6 women and 8 boys so that the share of a man, a woman and a boy are in the ratio 3: 2: 1. Then, how much does a man get? (In Rs.) 

Given:

Total amount = ₹1040

Number of men = 2

Number of women = 6

Number of boys = 8

Ratio of shares of a man, a woman, and a boy = 3:2:1

Formula used:

Total ratio = (Number of men × share of a man) + (Number of women × share of a woman) + (Number of boys × share of a boy)

Individual share = \(\dfrac{\text{Total amount} \times \text{Individual ratio}}{\text{Total ratio}}\)

Calculations:

Total ratio = (2 × 3) + (6 × 2) + (8 × 1)

⇒ Total ratio = 6 + 12 + 8

⇒ Total ratio = 26

Share of a man = \(\dfrac{\text{Total amount} \times \text{Individual ratio of man}}{\text{Total ratio}}\)

⇒ Share of a man = \(\dfrac{1040 \times 3}{26}\)

⇒ Share of a man = ₹120

∴ The correct answer is option (4).