2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 women alone to finish the work , and also that taken by 1 man alone.

Let the number of days taken by a woman and a man be x and y.

⇒ 4(2/x + 5/y) = 1

⇒ 2/x + 5/y = 1/4

⇒ 3(3/x + 6/y) = 1

⇒ 3/x + 6/y = 1/3

Putting 1/x = p and 1/y = q in these equations,

we get ⇒ 2p + 5q = 1/4

By cross multiplication, we get

⇒ p/-20 – (-18) = q/-9 – (-18)

= 1/144b- 180 ⇒ p/-2

= q/-1 = 1/-36 ⇒ p/-2

= – 1/36 and q/-1 = 1/-36

⇒ p = 1/18 and q = 1/36

⇒ p = 1/x = 1/18 and q = 1/y = 1/36

⇒ x = 18 and y = 36

Number of days taken by a woman = 18

Number of days taken by a man = 36

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