A and B together can do a piece of work in 20 days. A worked for 15 days and left. B finished the remaining work alone in 42 days. In how many days can B finish the whole work alone?
Show answer & explanation
Correct answer: C
Explanation
1/20 = A + B
Work done by A in 15 days = 15A
Remainder = 1 − 15A = 42B
⇒ 1 − 15A = 42B
⇒ 1 − 15A = 42(1/20 − A)
⇒ 1 − 15A = 42/20 − 42A
⇒ 1 − 15A = 21/10 − 42A
⇒ 1 − 21/10 = −42A + 15A
⇒ −11/10 = −27A
⇒ A = 11/270
⇒ B = 1/20 − 11/270 = 1/108 = 108 days