GATE CE 2016 Set 2 — Question 10
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Question
Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
Correct answer
(C) 3
Solution
Let be the total number of pages in the book. Ananth's reading rate is pages per hour.
Bharath's reading rate is pages per hour.Let be the time in hours after which the condition is met.
The number of pages remaining to be read by Ananth after hours is:
The number of pages remaining to be read by Bharath after hours is:
According to the problem, :
Dividing both sides by :
Rearranging the terms to solve for :
hours.Thus, after 3 hours, the number of pages to be read by Ananth is twice that of Bharath.
Bharath's reading rate is pages per hour.Let be the time in hours after which the condition is met.
The number of pages remaining to be read by Ananth after hours is:
The number of pages remaining to be read by Bharath after hours is:
According to the problem, :
Dividing both sides by :
Rearranging the terms to solve for :
hours.Thus, after 3 hours, the number of pages to be read by Ananth is twice that of Bharath.
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