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 remaining to be read by Ananth, twice that the number of pages remaining to read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 3 : 3

Let the number of pages of the book be n.

Given,

Time needed To read a book

Ananth takes 6 hours

Bharath takes 4 hours 

∴ Number of pages read in 1 hour

Ananth reads n/6 pages

Bharath reads n/4 pages 

Number of pages remaining to be read

Number of pages remaining to be read by Ananth = \(n - \frac{{nt}}{6} \)

Number of pages remaining to read by Bharath = \(n - \frac{{nt}}{4}\)

Let after ‘t’ hours the number of pages remaining to be read by Ananth is twice that number of pages remaining to read by Bharath.

(Number of pages remaining to be read by Ananth) = 2 × (Number of pages remaining to read by Bharath)

\(\therefore n - \frac{{nt}}{6} = 2\left( {n - \frac{{nt}}{4}} \right)\)

⇒ 1 – t/6 = 2 – t/2

⇒ t/3 = 1

⇒ t = 3 hours