Question

A, B, and C can do a work separately in 18, 36 and 54 days, respectively. 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?

• A. 12
• B. 13
• C. 15
• D. 14

Answer 1

Answer:

B. 13

Solution: GIVEN: A, B, and C can do work separately in 18, 36, and 54 days and they started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work CONCEPT USED: L.C.M of number of days = Total work FORMULA USED: Efficiency = Total work/Number of days CALCULATION: A, B, and C can do work separately in 18, 36, and 54 days ⇒ Total work = L.C.M (18, 36, and 54) = 108 ⇒ Efficiency = Total work/Number of days ⇒ Efficiency of A = 108/18 = 6 ⇒ The efficiency of B = 108/36 = 3 ⇒ The efficiency of C = 108/54 = 2 Suppose, B and C doesn't leave till the work get completed ⇒ Work of B and C for 5 days and 10 days = (5 × 3 + 2 × 10) ⇒ 35 ⇒ Now Total work = 108 + 35 = 143 ⇒ Number of days required to complete the whole work when they start working together = Total work/Efficiency(A + B +C) ⇒ 143/(6 + 3 + 2) ⇒ 143/11 ⇒ 13 ∴ The required number of days to complete the whole work when they start working together is 13 days