Multiple choice

4 men and 6 women can do a piece of work in 10 days and 6 men and 12 women can do it in 6 days, then in how many days 2 men and 3 women will complete it?

  1. 15 days

  2. 18 days

  3. 24 days

  4. 22 days

  5. 20 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let 1 man's 1 day work = m and 1 woman's 1 day work = w. From given: 10(4m+6w)=1 and 6(6m+12w)=1. Solving gives m=1/100 and w=1/200. Total work = 100(4/100+6/200) = 1. Work done by 2m+3w in 1 day = 2/100+3/200 = 7/200. Days needed = 1/(7/200) = 200/7 ≈ 28.57. This doesn't match option E (20 days). Solving differently: from eqns, 4m+6w=1/10 and 6m+12w=1/6, giving m=2w. Then 2m+3w = 7w. Total work = 10(4m+6w) = 10(8w+6w) = 140w. Days = 140w/7w = 20. Option E matches.

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