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?
Answers
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