Answer :

Let the number of days in which 1 woman and 1 man can do the work be ‘a’ and ‘b’ days respectively.


In 1 day, 1 woman completes 1/a part while 1 man does 1/b part


Given, 2 Women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days.


------ (1)


-------(2)


Multiplying eq1 by 3 and eq2 by 2

 

subtracting eq3 from eq4


⇒ 3/b = 1/12


⇒ b = 36 days


Thus, 3/a + 1/6 = 1/3


⇒ 3/a = 1/6


⇒ a = 18 days
Hence, A women can finish the embroidery in 18 days and A single man can finish the embroidery in 36 days

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