Question

a b can do a piece of work in 20 days. after 15 days a left the work then b finished it in 21 days. how many days a done that alone?​

Answer 1

Answer:

1/20th in 1 day. Correct

Step-by-step explanation:

Let A take x days to do the work alone. It means A does (1/x)th of the work in 1 day. So in 15 days, A does (15/x)th of the work.

Let B take y days to do the work alone. It means B does (1/y)th of the work in 1 day. So in 21 days, B does (21/y)th of the work.

A and B do the work in 20 days. It means A and B do (1/20)th of the work in 1 day.

Thus, (1/x)+(1/y) = (1/20), or

20x+20y = xy …(1)

15/x + 21/y = 1, or

21x+15y = xy …(2)

Or equating (1) and (2), 20x+20y = 21x+15y, or

x = 5y. Putting that in (1)

100y+20y = 5y^2, or

120y = 5y^2 or

y = 24. So, B takes 24 days to the work alone.

21x +360 = 24x, 3x = 360 or x = 120. So A alone will do the work in 120 days.

Check: So A and B do (1/120)+(1/24) = (1+5)/120 = 6/120 = 1/20th in 1 day. Correct