A, B, and C can do a piece of work in 42, 56, and 63 days respectively. They started the work together but A left the work 10 days before the completion of the work while B left the work 12 days before the completion. Find the number of days (approximate) to complete the whole work.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 25 days
Given that
A can do a piece of work alone in 42 days
B can do a piece of work alone in 56 days
C can do a piece of work alone in 63 days
Total work = LCM (42, 56, 63) = 504 days
The efficiency of A = 504/42 = 12
B = 504/56 = 9 and C = 504/63 = 8
Let the number of days to complete this work be d days
According to the question
⇒ A × (d - 10) + B × (d - 12) + C × d = 504
⇒ 12 × (d - 10) + 9 × (d -12) + 8 × d = 504
⇒ 12d - 120 + 9d - 108 + 8d = 504
⇒ 29d = 732
d = 732/29 = 25 days (approximate)