Time and work [समय और काम]-02

Question: I can finish a work in 15 days at 8 hrs a day. You can finish it in (6 and 2/3) days at 9 hrs a day. Find in how many days we can finish it working together 10 hrs a day. [मैं 8 घंटे प्रति दिन काम करते हुए किसी काम को 15 दिनों में कर सकता हूँ. आप 9 घंटे प्रति दिन काम करते हुए उसे (6 तथा 2/3) दिनों में कर सकते हैं. 10 घंटे प्रति दिन काम करते हुए हम दोनों उस काम को कटने दिनों में पूरा कर लेंगे?] [Ans. (b) 4 days]

(a) 8 days   (b) 4 days   (c) 6 days   (d) 9 days   (e) None of these

Solution:

Detailed Explanation: At the rate of 8 hours per day, 15 days contains 15×8 = 120.

Similarly, at the rate of 9 hours per day, (6 and 2/3) days = 20/3 days contains 9×20/3 hours = 60 hours.

First Method: 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

Here, I and You means “we” can do the whole work in: 120×60/(120 + 60) = 40 hours. But, work is to be done at the rate of 10 hours/day, so time taken is 40 hours/10 h/d = 4 days. Ans.

Second Method: I can do 1/120^th of the work in one hour; where as you can do 1/60^th of the work in one hour. Both together (I + You) can do (1/120) + (1/60) = 1/40^th work in one hour. Therefore, we can do the whole work in 40 hours. But, work is to be done at the rate of 10 hours/day, so time taken is 40 hours/10 h/d = 4 days. Ans.