A, B and C can do a piece of work in 15 days, 30 days and 40 days, respectively. A starts working on the first day, A and B works on the second day and A and C works on the third day. This pattern is repeated till the work gets completed. In how many days will the work be over?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 11.
Total work = LCM of (15, 30, 40) = 120 units
Efficiencies
A = 120 ÷ 15 = 8 units/day
B = 120 ÷ 30 = 4 units/day
C = 120 ÷ 40 = 3 units/day
Day 1: A = 8
Day 2: A + B = 8 + 4 = 12
Day 3: A + C = 8 + 3 = 11
Total in 3 days = 8 + 12 + 11 = 31 units
Work in 9 days = 31 × 3 = 93 units
Remaining = 120 − 93 = 27 units
Day 10: A = 8 → total = 93 + 8 = 101 → remaining = 19
Day 11: A + B = 12 → total = 101 + 12 = 113 → remaining = 7
Day 12: A + C = 11 → need 7 out of 11 → time = 7/11 day
So total time = 11