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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.

  1. $1$
  2. $2$ 
  3. $3$ 
  4. $4$
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6 Answers

Best answer
16 votes
16 votes
Assume the book is of $240$ pages.

Ananth reads $40$ pages per hour and Bharath reads $60$ pages per hour.

Number of pages Ananth will complete at the end of each hour $- 40, 80, 120, 160, 200, 240.$

Number of pages Bharath will complete at the end of each hour $- 60, 120, 180, 240.$

At the end of $3^{rd}$ hour, Bharath is left with $60$ pages and Ananth is left with $120$ pages.

So, $3$ is the answer.

Correct Answer: $C$
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7 votes
7 votes
After 3 hrs,

Ananth reads 3/6 of the book = 50% of the book --> Ananth is yet to read remaining 50% of the book.

Bharath reads 3/4 of the book = 75% of the book --> Bharath is yet to read remaining 25% of the book.

So after 3 hrs, Ananth has to read twice of what Bharath needs to read to complete the book.
3 votes
3 votes

Let there be $24$(multiple of (6,4)) pages in the book.

Ananth takes $6$ hours to read $24$ pages  $\Rightarrow$ Ananth takes $1$ hour to read $4$ pages.i.e. $20$ pages still left to read

Bharath takes $4$ hours to read $24$ pages $\Rightarrow$ Bharath takes $1$ hour to read $6$ pages i.e.$18$ pages still left to read


After how many hours number of pages to be read by Ananth, twice that to be read by Bharath.

Option $A.$ $1$ hour

It is not the answer since $20 \neq 2*18$


Option $B.$ $2$ hour

In $2$ hour Ananth will read $8$ page so $16$ pages will be left

In $2$ hours Bharath will read $12$ pages and $12$ pages will be left.

$\because$ $16 \neq 2*12$

$\therefore$ Option $B$ is not the answer


Option $C.$ $3$ hour

In $3$ hours Ananth will read $12$ page so $12$ pages will be left

In $3$ hours Bharath will read $18$ pages and $6$ pages will be left.

$\because$ $12 =2*6$

$\therefore$ Option $C$ is the correct answer


$\therefore$ Option $C.$ $3$ is the correct answer

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2 votes
2 votes
Ans: Option C

Let the book have x pages. In 1 hour, Ananth reads $\frac{x}{6}$ pages and Bharath reads $\frac{x}{4}$ pages. In h hours, Ananth and Bharath read $\frac{hx}{6}$ and $\frac{hx}{4}$ pages respectively. Also they are left with x – $\frac{hx}{6}$ and x – $\frac{hx}{4}$ pages yet to read after h hours. We want to find value of h for which

x – $\frac{hx}{6}$ = 2(x – $\frac{hx}{4}$)

Solving for h, we get h = 3.
Answer:

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