Time and work Quantitative aptitude question

[Q] P is thrice as good as workman as Q and therefore is able to finish a job in 60 days less than Q. Working together, they can do it in:
(a) 20 ½ days
(b) 22 ½ days
(c) 21 ½ days
(d) 23 ½ days

Solution

Answer   (b)
Explanation
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If P completes a work in 1 day, Q completes the same work in 3 days

Hence, if the difference is 2 days, Q can complete the work in 3 days

=> if the difference is 60 days, Q can complete the work in 90 days

=> Amount of work Q can do in 1 day= 1/90

Amount of work P can do in 1 day = 3 × (1/90) = 1/30

Amount of work P and Q can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> P and Q together can do the work in 45/2 days = 22 ½ days