Question 67

A work is completed by P and Q working together 8 hours perday. Working 8 hours a day P alone will take 12 days to complete work, while working alone Q will take 10 days working 12 hoursa day,to complete it. In how manydays did they complete the work together?

Solution

P can complete the work in (12 x 8) hrs = 96 hrs

Q can complete the work in (10 x 12) hrs=120 hrs

Therefore, P's 1 hour work=1/96 and Q's 1 hour work= 1/120

(P+Q)'s 1 hour's work =(1/96) + (1/120) = 9/480. So both P and Q will finish the work in 480/9 hrs

Therefore, Number of days of 8 hours each = (480/9) x (1/8) = 60/9

$$6\frac{2}{3}$$ days

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