Correct Answer - Option 3 : 22 days
Given:
Rajesh can do the work in 36 days
Rakesh can do the same work in 54 days
Ramesh can do the same work in 72 days
Rajesh, Rakesh and Ramesh together worked for 13 days
Ramesh alone worked for 4 days
Calculation:
Rajesh's 1 day work = 1/36
Rakesh's 1 day work = 1/54
Ramesh's 1 day work = 1/72
If all three worked together for 1 day then total work done = (1/36) + (1/54) + (1/72) = 13/216
If all three worked together for 13 days then total work done = 13 × (13/216) = 169/216
Rakesh left the job 4 days before the completion of the work so Ramesh alone worked for 4 days.
∴ Ramesh's 4 days work = 4 × (1/72) = 4/72
Total work done till now = (169/216) + (4/72) = 181/216
Work left to be done = 1 - (181/216) = 35/216
This left work is done by Rakesh and Ramesh.
Let they had done this amount of work in x days
∴ x × {(1/54) + (1/72)} = 35/216
⇒ x × (7/216) = 35/216
⇒ x = 5
∴ Total no. of days required to dug the well = 13 + 5 + 4 = 22 days