2women and 5 men can together …
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Yogita Ingle 5 years, 7 months ago
Let 1 woman can finish the embroidery work in 'x' days and 1 man can finish it in 'y' days.
A woman's one day work = 1/x
and a man's one day work = 1/y
A.T.Q.
2/x + 5/y = 1/4 and
3/x + 6/y = 1/3
Let 1/x = a and 1/y = b
Now, 2a + 5b = 1/4 _(1)
and 3a + 6b = 1/3 _(2)
Multiplying _(1) by 3 and _(2) by 2 and subtracting
6a + 15b = 1/4
6a + 18b = 1/3
___________
0 + 3b = 1/4 - 1/3
=> 3b = 1/12
=> b = 1/(12×3)
=> b = 1/36
Putting b = 1/36 in _(1)
2a + 5(1/36) = 1/4
=> 72a + 5 = 36/4
=> 72a + 5 = 9
=> 72a = 9 - 5
=> 72a = 4
=> a = 4/72
=> a = 1/18
Now, a = 1/x = 1/18
=> x = 18
And, b = 1/y = 1/36
=> y = 36
So, 1 woman can finish the embroidery work in 18 days and 1 man can finish the work in 36 days.
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