Exams › SSC CGL (Prelims) › General

The efficiency of A, B and C is in the ratio 2:3:5. A alone can complete the work in 40 days. They all worked together for 5 days and then C left the work. In how many days can A and B together complete the remaining work?

1. 12 days
2. 10 days
3. 8 days
4. 6 days

Correct answer: 6 days

Solution

Since A:B:C = 2:3:5 and A alone finishes in 40 days, A's rate is 1/40 work/day, so 2 parts = 1/40 and 1 part = 1/80. Thus B's rate = 3/80 and C's rate = 5/80. Together they work at 2/80 + 3/80 + 5/80 = 10/80 = 1/8 per day, so in 5 days they complete 5/8 of the work; remaining work = 3/8. A and B together work at 1/40 + 3/80 = 1/16 per day, so time needed = (3/8) ÷ (1/16) = 6 days.

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