A and B can complete a certain task in 24 days and 40 days, respectively. They worked together for 8 days. C completed the remaining task in 14 days. Working together, A and C will complete 75% of the same work in:
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10 days
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9 days
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15 days
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12 days
A
Correct answer
Explanation
A's rate = 1/24 per day, B's rate = 1/40 per day. Working together for 8 days: 8(1/24 + 1/40) = 8(5/120 + 3/120) = 8(8/120) = 64/120 = 8/15 of work done. Remaining = 7/15. C completes 7/15 in 14 days, so C's rate = (7/15)/14 = 1/30 per day. A and C together: 1/24 + 1/30 = 5/120 + 4/120 = 9/120 = 3/40 per day. For 75% (3/4) of work: Time = (3/4)/(3/40) = (3/4) × (40/3) = 10 days. Option A is correct.