Question

The ratio of the speeds of two trains is 7:8. If the second train covers 400km in 4 hours, then the speed of the first train is
[a] 70 km/hr
[b] 75 km/hr
[c] 84 km/hr
[d] 87.5 km/hr

Answer 1

Hint: Since the ratio of speeds is 7:8, assume that the speed of the first train is 7x and that of the second train is 8x. Now using $\text{speed=}\dfrac{\text{Distance covered}}{\text{time taken}}$ , find the time taken by the second train to cover 400Km. Equate this time to be equal to 4 hours. Hence form an equation in x. Solve for x. Hence find the speed of the first train.

Complete step-by-step answer:

Let the speed of the first train be 7x Km/hr and that of the second train be 8x Km/hr.
Given that the time taken by the second train to cover 400 km = 4 hours.
Hence, we have $\dfrac{400}{8x}=4$
Multiplying both sides by 8x, we get
$\begin{align}
  & \dfrac{400}{8x}8x=8x(4) \\
 & \Rightarrow 100=8x \\
\end{align}$
Dividing both sides by 8, we get
$\begin{align}
  & \dfrac{100}{8}=\dfrac{8x}{8} \\
 & \Rightarrow \dfrac{25}{2}=x \\
\end{align}$
Hence, we have $x=\dfrac{25}{2}$.
Now the speed of the first train $=7x$.
Substituting $x=\dfrac{25}{2}$, we get
The speed of the first train $=7\left( \dfrac{25}{2} \right)=\dfrac{175}{2}=87.5$
Hence the speed of the first train = 87.5 Km/hr.
Hence option [d] is correct.
Note: Since the ratio of speeds of first train to second is 7:8, the speed of the first train is $\dfrac{7}{8}$ time the speed of the second train.
Now we have,
Distance covered by second train = 400 km.
Time taken to cover the distance = 4km.
Hence the speed of the train $=\dfrac{400}{4}=100$ Km/hr.
Hence the speed of the first train $=\dfrac{7}{8}\times 100=\dfrac{700}{8}=87.5$ km/hr.
Hence option [d] is correct.