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P alone can do a piece of work in 24 days. The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work. How many days are required to complete by P and Q working together ?

Correct Answer: 9 3/5 days

Explanation:

Let the total work be 'W'


As per the given information,


P can complete the work 'W' in 24 days.


=> one day work of P = W/24


And also given that,


The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work


=> PW/3 = QW/2


=> P's


1 day =    W/24


   ?    =      W/3


=>  ?  = 24W/3W  = 8


=> QW/2 = 8 days


=> Q alone can complete the work W in 16 days


=> P + Q can complete the work in


1/24 + 1/16 = 5/48


=> 48/5 days = 9 3/5 days.


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