Concept of “Time and Work”-06

Question: I can finish a work in 16 days at 5 hrs a day. You can finish it in 12 days at 4 hrs a day. Find in how many days we can finish it working together 6 hrs a day.   [Ans. (a) 5 days]

(a) 5 days  (b) 4 days (c) 6 days (d) 8 days  (e) None of these

Solution: 

Detailed Explanation:

Concept: If A can do a work in “x” hours and B can do the same work in “y” hours; then A and B together can do the same work in xy/(x+y) hours

No. of hours in 16 days at the rate of 5 hrs/day = 16×5 hrs = 80 hrs

Also, no. of hours in 12 days at the rate of 4 hrs/day = 12×4 hrs = 48 hrs

I can finish a work in 80 hrs (since I can finish a work in 16 days at 5 hrs a day) and you can finish the same work in 48 hrs (since you can finish the same work in 12 hrs at the rate of 4 hrs/day).

A and B together can finish the whole work in (80×48)/128 hrs = 30 hours

But, both work at 6 hours/day, so the work will be finished in 30 hrs/6hrs/day = 5 days Ans.