A, B, and C can finish a task in 42 days, 84 days, and 28 days, respectively. A started the work and B joined him after 3 days. If C joined them after 5 days from the beginning, then for how many days did A work till the completion of the task?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 17.
Suppose total work = 84 (LCM of 42, 84 and 28)
Now,
Efficiency of A = 84/42 = 2
Efficiency of B = 84/84 = 1
Efficiency of C = 84/28 = 3
Since A started the work B joined him after 3 days and C joined them after 5 days from the beginning:
Then A worked for x days, B for (x – 3) days and C for (x – 5) days:
2x + 1(x – 3) + 3(x – 5) = 84
⇒ 6x = 84 + 18
⇒ 6x = 102
⇒ x = 17
Hence, A worked for 17 days