Discussion

Explanation:

20 men can complete a task in 3 days, 10 women can complete the same task in 4 days while 60 boys can complete the same task in 2 days. How long will it take for 2 men, 2 women and 5 boys to complete the task together.

Let the efficiency of a man be 'm' units/day, that of a woman be 'w' units/day and that of a boy be 'b' units/day.

20 men can complete the task in 3 days ⇒ Work done = 20m × 3 = 60m   ...(1)
10 women can complete the task in 4 days ⇒ Work done = 10w × 4 = 40w   ...(2)
60 boys can complete the task in 2 days ⇒ Work done = 60b × 2 = 120b   ...(3)

Since work done is same in all these cases
⇒ 60m = 40w = 120b
⇒ 3m = 2w = 6b   ...(4)

Let 2 men, 2 women and 5 boys complete the task in d days ⇒ Work done = (2m + 2w + 5b) × d   ...(5)

Now, (5) = (3)
⇒ (2m + 2w + 5b) × d = 120b
⇒ (4b + 6b + 5b) × d = 120b [from (4)]
⇒ 15b × d = 120b
⇒ d = 8 days.

Hence, option (b).

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