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In a school, a Science project has been assigned to three students Rajat, Rohan, and Bishal and it was told that they should work together on that project. Working alone Rohan can finish the project in 20 days, it is also given that if Rajat and Bishal work on the project they will take 9 days to complete the project. Bishal alone can complete the project in 15 days. Rohan started working on the project from Monday but after 8 days he left and after that Rajat and Bishal started working on it but Bishal also left 6 days before completion of the work and Rajat completed the remaining project, in how many days will the project be completed and on which day will it be completed?

In a school, a Science project has been assigned to three students Rajat, Rohan, and Bishal and it was told that they should work together on that project. Working alone Rohan can finish the project in 20 days, it is also given that if Rajat and Bishal work on the project they will take 9 days to complete the project. Bishal alone can complete the project in 15 days. Rohan started working on the project from Monday but after 8 days he left and after that Rajat and Bishal started working on it but Bishal also left 6 days before completion of the work and Rajat completed the remaining project, in how many days will the project be completed and on which day will it be completed? Correct Answer 17 days, Thursday

Given:

Rohan can complete the project in 20 days

Rajat and Bishal together can complete it in 9 days.

Bishal alone takes 15 days to complete the project.

Concept:

Efficiency = Total work/Total time

Calculation:

The L.C.M of 20, 9, and 15 is 180

⇒ Efficiency of Rohan = 180/20 = 9

⇒ Efficiency of Rajat and Bishal = 180/9 = 20

⇒ Efficiency of Bishal = 180/15 = 12

Efficiency of Rajat is (20 – 12) = 8

At first, Rohan will work for 8 days

So he will do 9 × 8 = 72 units

So remaining (180 - 72) = 108 units is to be done by Rajat and Bishal.

Bishal has left 6 days before completion of the project.

So last 6 days only Rajat will work

Rajat alone will do 6 × 8 = 48 units

So remaining (108 - 48) = 60 units have been completed by Rajat and Bishal in 60/20

⇒ 3 days

Total time taken by all of them is 8 + 3 + 6 = 17 days

∴ In 17 days the project be completed and on Thursday will it be completed.

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