X takes 4 days to complete one-third of a job. Y takes 3 days to complete one-sixth of the job and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.

A. 6 days

B. 8.1 days

C. 5.1 days

D. 7 days

E. None of these

Answer: Option C

Solution(By Examveda Team)

X completes $$\frac{1}{3}$$ rd in 4 days = 33.33% job in 4 days
X One day work = 8.33%
Y one day work = 5.55% [As he complete $$\frac{1}{6}$$ job = 16.66% job in 3 days]
Z one day work = 10%
Work done in 3 days by X, Y and Z
= 25 + 16.66 + 30 = 71.66%
Remaining work will be done by Y in,
$$\frac{{28.33}}{{5.55}}$$  = 5.1 days