X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning, them for how many days did X worked?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18
X, Y, and Z can do a piece of work in 46 days, 92 days, and 23 days respectively.
Work finished by X in 1 day = 1/46
Work finished by Y in 1 day = 1/92
Work finished by Z in 1 day = 1/23
Work finished by X and Y in 1 day = 1/46= (1/46) + (1/92) = 3/92
Work X, Y, and Z can finish together in 1 day = (1/46) + (1/92) + (1/23) = 7/92
Work X can do in 2 days = 2/46 = 1/23
Work X and Y can do in 6 days = 6(3/92) = 9/46 [Z joined them after 8 days from the beginning]
The remaining work = 1 - [(1/23) + (9/46)] = 1 - (11/46) = 35/46
Time is taken by X, Y, and Z to finish the work = (35/46)/(7/92) = (35/46) × (92/7) = 10 days
Total time of work of X = 8 + 10 = 18 days