Anil and Karan together can do a work in 20 days. Karan and Himanshu together can do the same work in 25 days. Himanshu and Anil together can do the same work in 50 days. In how many days can Himanshu alone do the same work?

Correct option is D

Given:
Anil and Karan can complete work in 20 days
Karan and Himanshu can complete work in 25 days
Himanshu and Anil can complete work in 50 days
Formula Used:
Work done per day = Total work / Number of days
Efficiency of each pair = 1 / Number of days taken by the pair to complete the work.
Solution:
LCM(20, 25, 50) = 100 units of work.
Anil and Karan's efficiency = 100 / 20 = 5 units/day
Karan and Himanshu's efficiency = 100 / 25 = 4 units/day
Himanshu and Anil's efficiency = 100 / 50 = 2 units/day
(Anil + Karan) + (Karan + Himanshu) + (Himanshu + Anil) = 5 + 4 + 2 = 11 units/day
2(Anil + Karan + Himanshu) = 11
Anil + Karan + Himanshu = 11 / 2 = 5.5 units/days
Anil + Karan = 5 units/day
So, Himanshu's efficiency = (Anil + Karan + Himanshu) - (Anil + Karan)
Himanshu's efficiency = 5.5 - 5 = 0.5 units/day
Therefore, Himanshu will take 100 / 0.5 = 200 days to complete the work alone.