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 ?
A) 9 3/5 days
B) 7 days
C) 6 3/7 days
D) 8 days
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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
=> QW = 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........(A)
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