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In Bhitari village a well has to be dug. Rajesh, Rakesh and Ramesh can dig the well in 36 days, 54 days and 72 days respectively. All three started digging the well together but due to some reason, Rajesh left the work after 13 days of starting the work and Rakesh left the work 4 days before the completion of the work. Find the time taken in which the well has been dug.
1. 5 days
2. 17 days
3. 22 days
4. 27 days

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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

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