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.
The total number of days = n
A, B, and C can complete a work in 30, 60, and 120 days respectively
L.C.M(30, 60, and 120) = 120
The efficiency of A = 120/30 = 4 units
The efficiency of B = 120/60 = 2 units
The efficiency of C = 120/120 = 1 units
Now, according to the question
⇒ 4(n - 10) + 2(n - 5) + 1n = 120
⇒ 4n - 40 + 2n - 10 + n = 120
⇒ 7n - 50 = 120
⇒ 7n = 170
⇒ n = 170/7
Hence, the number of days required to complete the whole work = 170/7 days