Question : 20 women and 15 men together can complete a work in 6 days. It takes 150 days for a single woman to complete the work. In how many days can a single man complete the work?
Option 1: 450
Option 2: 225
Option 3: 350
Option 4: 210
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Correct Answer: 450
Solution :
Let $w$ and $m$ be women and men respectively.
Given:
20 women and 15 men can complete a work in 6 days.
A single woman can complete a work in 150 days.
Total work is the same in both cases.
$(20w +15m)\times 6 = 150 \times 1w$
⇒ $20w+15m = 25w$
⇒ $15 m = 5 w$
⇒ $3m = 1w$
Let one man work 1 unit in a day and 1 woman 3 units work in a day.
Total work = $[20(3) + 15(1)]\times 6 = 75\times 6 = 450$ units
$\therefore$ A single man will complete the work in 450 days since a man does 1 unit of work in a day.
Hence, the correct answer is 450.
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