Time and work Quantitative aptitude question

[Q] X takes twice as much time as Y or thrice as much time as Z to finish a piece of work. If Working together, they can finish the work in 2 days. Then, working alone, how many days will Y take to complete the work?
(a) 5 days
(b) 6 days
(c) 4 days
(d) 7 days

Solution

Answer   (b)
Explanation
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Let X takes x days to complete the work,

Then Y takes x/2 days and Z takes x/3 days to complete the work

Amount of work X does in 1 day = 1/x

Amount of work Y does in 1 day = 2/x

Amount of work Z does in 1 day = 3/x

Amount of work X,Y and Z do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

6/x = 2

=> x = 12

=> Y takes 12/2 days = 6 days to complete the work