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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