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.