Question : A and B together can do a piece of work in 12 days. A alone can do it in 18 days. In how many days B alone can do the work?
Option 1: 36 days
Option 2: 24 days
Option 3: 32 days
Option 4: 30 days
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Correct Answer: 36 days
Solution : A and B together can do a piece of work in = 12 days. A alone can do the same work in = 18 days. Time = $\frac{\text{Total work}}{\text{Efficiency}}$ Total work = Least Common Multiple of 12 and 18 = 36 units Efficiency of (A + B) = $\frac{36}{12}$ = 3 Efficiency of A = $\frac{36}{18}$ = 2 Efficiency of B = Efficiency of (A + B) - Efficiency of A = (3 - 2) = 1 unit/day Time taken by B = Total work/Efficiency = 36/1 = 36 days $\therefore$ B alone can do the work in 36 days. Hence, the correct answer is 36 days.
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