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
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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