One man two women can complete a task in 12 days, while 5 men and 3 women can complete the same task in 6 days. How many days will it take 7 men and 6 women to complete the same task?
Explanation:
Let the efficiency of man be 'm' units/day and that of a woman be 'w' units/day
Work done by a man and two women in 12 days = (m + 2w) × 12 Work done by 5 men and 2 women in 6 days = (5m + 2w) × 6 Work done by 7 men and 6 women in d days = (7m + 6w) × d
Since the work done is same in all these cases.
⇒ (m + 2w) × 12 = (5m + 2w) × 6 = (7m + 6w) × d
Equating first 2 expressions ⇒ (m + 2w) × 12 = (5m + 2w) × 6 ⇒ 2m + 4w = 5m + 2w ⇒ 2w = 3m
Now equating last 2 expressions ⇒ (5m + 2w) × 6 = (7m + 6w) × d [Substitute 2w = 3m] ⇒ (5m + 3m) × 6 = (7m + 9m) × d ⇒ 8m × 6 = 16m × d ⇒ d = 3
Hence, 3.
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