Q263 / 270 · NDA 2018 (Phase 1) · Mathematics
A train covers the first 5 km of its journey at a speed of 30 $\mathrm{km} / \mathrm{hr}$ and the next 15 km at a speed of $45 \mathrm{~km} / \mathrm{hr}$. What is the average speed of the train?
- A$35 \mathrm{~km} / \mathrm{hr}$
- B$37.5 \mathrm{~km} / \mathrm{hr}$
- C$39.5 \mathrm{~km} / \mathrm{hr}$
- Correct answerD$40 \mathrm{~km} / \mathrm{hr}$
Solution
Time taken by train to cover first $5 \mathrm{~km}=\frac{\text { Distance }}{\text { Speed }}$
$=\frac{5}{30}=\frac{1}{6} \mathrm{hr}$
Time taken by train to cover next $15 \mathrm{~km}=\frac{15}{45}=\frac{1}{3} \mathrm{hr}$.
$\begin{aligned}
& \text { Average speed }=\frac{5+15}{\frac{1}{6}+\frac{1}{3}} \\
& =\frac{20}{\frac{1+2}{6}}=\frac{120}{3}=40 \mathrm{~km} / \mathrm{hr}
\end{aligned}$
Hence, the correct answer is option: 'D'.