A and B can complete a certain work in 6 days and 8 days, respectively. They worked together for 3 days. C alone completed the remaining work in 2 days. B and C together can complete (\frac{3}{4}) of the same work in:
-
6 days
-
4 days
-
3 days
-
2 days
B
Correct answer
Explanation
A's rate = 1/6 work per day, B's rate = 1/8 work per day. Combined A+B rate = 1/6 + 1/8 = 7/24 per day. In 3 days together they complete 3 × 7/24 = 7/8 work. Remaining work = 1 - 7/8 = 1/8. C completes 1/8 work in 2 days, so C's rate = 1/16 per day. B+C combined rate = 1/8 + 1/16 = 3/16 per day. Time to complete 3/4 work = (3/4) / (3/16) = 4 days.