3 men and 7 women can complete a task in 10 days. On the other hand, 4 men and 6 women, take 8 days to complete the same task. How long will it take 10 women to complete the same task?
Explanation:
Let the efficiency of each man and woman is m and w respectivley.
∴ Work done by 3 men and 7 women in 10 days = work done by 4 men and 6 women in 8 days = work done by 10 women in say 'd' days.
⇒ (3m + 7w) × 10 = (4m + 6w) × 8 = 10w × d
Solving first two expressions, we get ⇒ (3m + 7w) × 10 = (4m + 6w) × 8 ⇒ 11w = m
Now, equating the last two expressions, we get ⇒ (4m + 6w) × 8 = 10w × d ⇒ (44w + 6w) × 8 = 10w × d ⇒ 400w = 10w × d ⇒ d = 40 days
Hence, option (d).