2 men and 4 boys can do a piece of work in 10 days while 4 men and 5 boys can do it in 6 days Men an...........

Quant (SSC) Time and work

2 men and 4 boys can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days. Men and Boys are paid wages according to their output. If the daily wage of a man is Rs. 40, then the ratio of daily wages of a man and a boy will be

5 : 3

5 : 2

7 : 4

7 : 3

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Explanation:

Men = m; Boys = b.
From the given infromation,
(2m + 4b) × 10 ≡ (4m + 5b) × 6
⇒ 20m + 40b ≡ 24m + 30b
⇒ 4m ≡ 10b
⇒ 2m ≡ 5b
∴ 5b = 2 × 40
⇒ 1b = 2 x 40/5 = 16
∴ Required ratio = 40 : 16 = 5 : 2