Question : A, B and C can work separately in 18, 36 and 54 days. They started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work. In how many days was the work finished?
Option 1: 15 days
Option 2: 13 days
Option 3: 14 days
Option 4: 12 days
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Correct Answer: 13 days
Solution :
A, B, and C can do work separately in 18, 36, and 54 days
Let the total work = LCM (18, 36, and 54) = 108 units
Efficiency = $\frac{\text{Total work}}{\text{Number of days}}$
So, Efficiency of A = $\frac{108}{16}$ = 6
Efficiency of B = $\frac{108}{36}$ = 3
Efficiency of C = $\frac{108}{54}$ = 2
Additional work that could have been done by B and C for 5 days and 10 days = 5 × 3 + 2 × 10 = 35
Total effective work = 108 + 35 = 143
The number of days required to finish the work = $\frac{\text{Total work}}{\text{Efficiency(A + B + C)}}$
= $\frac{143}{6 + 3 + 2}$
= $\frac{143}{11}$
= 13
Hence, the correct answer is 13 days.
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