# Ram and Shyam can complete a piece of work in 25 days, 40 days respectively they start the work together and before 14 days Ram leaves the work, In ho

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Ram and Shyam can complete a piece of work in 25 days, 40 days respectively they start the work together and before 14 days Ram leaves the work, In how many days they will finish work?

1. 28 days
2. 26 days
3. 24 days
4. 25 days
5. None of these

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Correct Answer - Option 3 : 24 days

Given:

Ram alone can complete work = 25 days

Shyam alone can complete work =  40 days

Ram and Shayam start the work together and before 14 days Ram leave the work

Concept:

Total work = Time × Efficiency

Calculation:

Let Total work = LCM(25, 40) = 200

 Work done Time taken (in the day) Efficiency Ram 25 200/25 = 8 Shyam 40 200/40 = 5 Total work = L. C. M. = 200

Last 14 day work done by Shyam = 5 × 14 = 70 unit

Remaining work for Ram and Shayam together = 200 – 70 = 130 unit

Efficiency of Ram and Shayam together = 8 + 5 = 13 unit

Number of days in which Ram and Shayam work together = 130/13 = 10 days

Total days to complete the work = 14 + 10 = 24 days

∴ Ram and Shayam finish work in 24 days.