Correct Answer - Option 2 : 13 days
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
