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2 women and 3 men can do a piece of work in 10 days while 3 women and 2 men can do the same work in 8 days. In how many days can 2 women and 1 man do the work?

Solution

Correct Option: 4

Let 1 woman's work =1W= \frac{1}{W} and 1 man's =1M= \frac{1}{M}. From 2W+3M=110\frac{2}{W} + \frac{3}{M} = \frac{1}{10} and 3W+2M=18\frac{3}{W} + \frac{2}{M} = \frac{1}{8}, solving gives 1W=7200,1M=1100\frac{1}{W} = \frac{7}{200}, \frac{1}{M} = \frac{1}{100}. Then 2W+1M=14200+2200=16200\frac{2}{W} + \frac{1}{M} = \frac{14}{200} + \frac{2}{200} = \frac{16}{200}. Days =20016=12.5= \frac{200}{16} = 12.5.

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