X1, X2, and X3 can do 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?(approximately)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 27 days.
Let the total work be one unit
X1 can complete the work in 90 days, X2 can complete the work in 45 days, and X3 can complete the work in 67.5 days.
So,
X1's work rate per day = 1/90 of the total work
X2's work rate per day = 1/45 of the total work.
X3's work rate per day = 1/67.5 of the total work
Let the total time taken is D days
Since X2 leaves 13.5 days before the work is completed, X2 works for D - 13.5 days
Now, according to the question
⇒ 1/90 × D + 1/45 × (D - 13.5) + 1/67.5 × D = 1
⇒ D/90 + 2(D - 13.5)/90 + 2D/135 = 1
⇒ D/90 + (2D - 27)/90 + 2D/135 = 1
⇒ (D + 2D - 27)/90 + 2D/135 = 1
⇒ (3D - 27)/90 + 2D/135 = 1
⇒ 3(3D - 27)/270 + 4D/270 = 1
⇒ (9D - 87)/270 + 4D/270 = 1
⇒ (9D - 87 + 4D)/270 = 1
⇒ 13D - 87 = 270
⇒ 13D = 357
⇒ D = 27.46 or 27 Days approximately
Hence, the work will be completed in 27 days