A and B together can do a work in 10 days. B and C together can do the same…
2021
A and B together can do a work in 10 days. B and C together can do the same work in 12 days. If C alone can do the same work in 60 days, then in how many days can A alone do the same work?
- A.
30 days
- B.
45 days
- C.
20 days
- D.
60 days
Attempted by 73 students.
Show answer & explanation
Correct answer: A
Solution: Let one complete job = 1. Convert given information to daily rates: A + B = 1/10 per day, B + C = 1/12 per day, C = 1/60 per day.
Find B: rate(B) = (B + C) − rate(C) = 1/12 − 1/60 = (5 − 1)/60 = 4/60 = 1/15 per day.
Find A: rate(A) = (A + B) − rate(B) = 1/10 − 1/15 = (3 − 2)/30 = 1/30 per day. So A takes 30 days to finish the job alone.
Check: rate(A) + rate(B) = 1/30 + 1/15 = 1/30 + 2/30 = 3/30 = 1/10, which matches the given A + B rate.
Answer: A alone can do the work in 30 days.