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Ravi, Manish and Naveen alone can complete a work in 30 days, 15 days and 10 days respectively. They start the work together but Ravi leaves the work after 2 days of the starting of the work and Manish leaves the work after 3 days more. In how many days Naveen will complete the remaining work?

Ravi, Manish and Naveen alone can complete a work in 30 days, 15 days and 10 days respectively. They start the work together but Ravi leaves the work after 2 days of the starting of the work and Manish leaves the work after 3 days more. In how many days Naveen will complete the remaining work? Correct Answer 1 day

Given:

Ravi can complete the work 30 days

Manish can complete it in 15 days

And Naveen can complete it in 10 days

Concept:

In this type of question always imagine the total work as LCM of time taken by individuals to

perform the work.

Formula used:

Efficiency = Total work/Time taken

Calculation:

Let the total work be LCM of 30, 15, 10 i.e. 30 unit

So efficiency of Ravi = 30/30 = 1 unit/day

Efficiency of Manish = 30/15 = 2 unit/day

Efficiency of Naveen = 30/10 = 3 unit/day

Ravi work for 2 days and performed work = 2 × 1 = 2 unit

Manish work for 5 days and performed work = 5 × 2 = 10 unit

Naveen 5 day work = 5 × 3 = 15 unit

Remaining work = 30 – (2 + 10 + 15) = 3 unit

∴ Time taken by Naveen to complete the remaining work = 3/3 = 1 day

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