Ashu reads at an average rate of 30 pages per hour while Neeru reads at an average rate of 40 pages per hour. If Ashu starts reading a novel at 2: 30 and Neeru begins reading an identical copy of the same book at 3: 20, at what time will they be reading the same page?
(a)5: 00
(b)5: 50
(c)6: 40
(d)7: 00
(e)7: 30
Answer
Answer (as printed): B
Explanation
Number of pages read by Ashu from 2: 30 to 3: 20 i.e., in 50 min or $\frac{5}{6} \mathrm{hr}=\left(\frac{5}{6} \times 30\right)=25$. Let the two read the same page $x$ hours after 3: 20. Then, pages read by Ashu $=(25+30 x)$. And, pages read by Neeru $=40 x$. $$\therefore \quad 25+30 x=40 x \Rightarrow x=\frac{5}{2}=2 \frac{1}{2} .$$ Hence, the two read the same page $2 \frac{1}{2}$ hours after 3: 20 i.e., at 5: 50.
Explanation as extracted from the printed page; notation may be imperfect.