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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

Answer: c
Explanation: 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,
$$\frac{{28.33}}{{5.55}}$$  = 5.1 days

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