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Question

2women and5 men can together finish an embroidery work in4 days, while3 women and6 men can finish it in3 days. Find the time taken by1 woman alone to finish the work, and also that taken by1 man alone.


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Solution

Find the time taken by1 woman alone to finish the work, and also that taken by1 man alone.

Let the number of days taken by a woman and a man bex andy.

42x+5y=12x+5y=14.......1

33x+6y=13x+6y=13.......2

Putting 1x=p and1y=q in these equations,

we get,

2p+5q=14From18p+20q=1......(3)

and

3p+6q=13From29p+18q=1........4

Multiply equation3 by9 and4 by8, we get

72p+180q=9......572p+144q=8......6

Subtract equation6 from5,

36q=1q=136

Then put the value ofq in equation4,

9p+18×136=19p+12=19p=1-129p=12p=118

p=1x=118andq=1y=136x=18andy=36

Number of days taken by a woman=18 and Number of days taken by a man=36


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