A, B, and C can complete a work in 30, 60, and 120 days, respectively. A left the work 10 days before the work was completed, and B left 5 days before the completion of the work. Find the number of days required to complete the whole work.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 170/7 days
Given that
A, B, and C can complete a work in 30, 60, and 120 days respectively.
Total work = LCM (30, 60, 120) = 120 days
The efficiency of A = 120/30 = 4
The efficiency of B = 120/60 = 2
The efficiency of C = 120/120 = 1
Let the whole work completed in d days
According to the question
A × (d - 10) + B × (d - 5) + C × d = 120
4 × (d - 10) + 2 × (d - 5) + 1 × d = 120
4d - 40 + 2d - 10 + d = 120
7d = 120 + 50 = 170
d = 170/7 days