Question

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
(a) 70 kmph
(b) 75 kmph
(c) 84 kmph
(d) 87.5 kmph

Answer 1

Hint: First, let the speed of the first train be 7x kmph and let the speed of the second train be 8x kmph. Then use the information that the second train runs 400 km in 4 hours to get $8x=\dfrac{400}{4}=100$. From this find the value of x. now multiply this value of x by 7 to find the final answer.

Complete step-by-step answer:
In this question, we are given that the ratio between the speeds of two trains is 7 : 8. The second train runs 400 km in 4 hours.

We need to find the speed of the first train.

Let the speed of the first train be 7x kmph and let the speed of the second train be 8x kmph.

We are given that the second train runs 400 km in 4 hours, therefore, we have the following:

$8x=\dfrac{400}{4}=100$

$x=\dfrac{100}{8}$

$x=12.5$

So, the speed of the second train is 8 $\times $ 12.5 = 100 kmph.

And the speed of the second train is 7 $\times $ 12.5 = 87.5 kmph.

So, option (d) is correct.

Note: In this question, it is very important to understand the ratio and then suppose that the speed of the first train is 7 x kmph and let the speed of the second train is 8 x kmph. Then you should be able to use the information that the second train runs 400 km in 4 hours properly to find the value of x.