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.
Options:
(A) 1
(B) 2
(C) 3
(D) 4
Official Answer Key:
C
Step-by-Step Solution & Explanation
• Let the book have 1 unit of reading volume.
• Reading rate of Ananth: $r_A = \frac{1}{6}$ books/hour.
• Reading rate of Bharath: $r_B = \frac{1}{4}$ books/hour.
• After $t$ hours:
- Remaining volume for Ananth: $1 - \frac{t}{6}$
- Remaining volume for Bharath: $1 - \frac{t}{4}$
• Condition: Pages remaining for Ananth is twice that for Bharath:
$1 - \frac{t}{6} = 2\left(1 - \frac{t}{4}\right)$
$1 - \frac{t}{6} = 2 - \frac{t}{2}$
$\frac{t}{2} - \frac{t}{6} = 2 - 1$
$\frac{3t - t}{6} = 1 \implies \frac{2t}{6} = 1 \implies t = 3 \text{ hours}$
• Verification at $t = 3$:
- Ananth has completed $3/6 = 0.5$, remaining = $0.5$.
- Bharath has completed $3/4 = 0.75$, remaining = $0.25$.
- $0.5 = 2 \times 0.25$. Matches exactly.
• Final Answer: (C) 3
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