12 men can complete a work in 10 days. 20 women can complete the same work in 12 days. 8 men and 4 women started working and after 9 days 10 more women joined them. How many days will they now take to complete the remaining work?
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2 days
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5 days
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6 days
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10 days
A
Correct answer
Explanation
12 men's rate = 1/10 work/day, so 1 man = 1/120. 20 women's rate = 1/12, so 1 woman = 1/240. 8 men + 4 women work for 9 days: (8/120 + 4/240) × 9 = (0.067 + 0.017) × 9 = 0.75 work done. Remaining = 0.25. New team: 8 men + 14 women = 8/120 + 14/240 = 0.067 + 0.058 = 0.125/day. Days needed = 0.25/0.125 = 2 days.