In the afternoon, a student read 100 pages at the rate of 60 pages per hour. In the evening, when she was tired, she read 100 more pages at the rate of 40 pages per hour. What was her average rate of reading the pages per hours ?
A. 60 B. 70 C. 48 D. 50 Answer: Option CShow Answer
Solution(By Apex Team)
According to the question,
Afternoon
100 pages read at the rate 60 pages per hour
Total time taken to read 100 pages
$\begin{array}{l}=\large\frac{100}{60}\\
=\large\frac{5}{3}\text{ hours }\\
\end{array}$
Evening 100 pages read at the rate 40 pages per hour Total time taken to read 100 pages $\begin{array}{l} =\large\frac{100}{40} \\ =\large\frac{5}{2} \text { hours } \end{array}$ Average rate of reading the pages per hour $\begin{aligned}&=\frac{200}{\frac{5}{3}+\frac{5}{2}}\\ &=\frac{200\times6}{10+15}\\ &=\frac{200\times6}{25}\\ &=48\end{aligned}$
Evening 100 pages read at the rate 40 pages per hour Total time taken to read 100 pages $\begin{array}{l} =\large\frac{100}{40} \\ =\large\frac{5}{2} \text { hours } \end{array}$ Average rate of reading the pages per hour $\begin{aligned}&=\frac{200}{\frac{5}{3}+\frac{5}{2}}\\ &=\frac{200\times6}{10+15}\\ &=\frac{200\times6}{25}\\ &=48\end{aligned}$
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