X1, X2 and X3 can do a work in 90, 45 and 67.5 days respectively. All three of them began the work together but X2 left 13.5 days before the completion of the work. In how many days was the work completed?

Correct option is D

Given: X1, X2, X3 efficiencies: 1/90, 1/45, 1/67.5, X2 left 13.5 days before completion.
Formula Used: Work done = Efficiency × Time
Solution:
Efficiency of X1 = 1/90
Efficiency of X2 = 1/45
Efficiency of X3 = 2/135
LCM of 90, 45 & 135 is 270.
Efficiency of X1, X2 & X3 = 3, 6 & 4
Work done by X2 in 13.5 days = 6 × 13.5 = 81
Work done = 270 + 81 = 351
∴ Required number of days = 351/13 = 27 days