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. Find the time taken by 1 woman alone to finish the embroidery, and that taken by 1 man alone.
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 and subtracting eq2 from eq1
⇒ 3/b = 1/12
⇒ b = 36 days
Thus, 3/a + 1/6 = 1/3
⇒ 3/a = 1/6
⇒ a = 18 days
16