Question

The ratio between the speeds of two trains is 7:10. If the second train runs 400km in 4 hours then the speed of the first train is (in km/hr)?

Answer 1

Hint: Suppose the speed of the first train as a variable and hence find the speed of the second train with the help of relation
 $ \text{speed}=\dfrac{\text{distance}}{\text{time}} $
Now, use both speeds and given ratio of speeds to get the value of speed of the first train.

Complete step-by-step answer:
Let the speed of the first train is v km/hr. As the distance 400km is covered by the second train in 4 hours, so we can calculate the speed of the second train using the relation given as
 $ \text{speed}=\dfrac{\text{distance}}{\text{time}}.................\left( i \right) $
So, we can put distance = 400km and time = 4 hours. So, we get speed of second train
 $ =\dfrac{400}{4}=100\text{km/hr} $
So, let speed of the second train is represented as u, so we get
u = 100km/hr……………(ii)
Now, we know the ratio of speed of both the trains is 7:10 as given in the problem. So, we can write the equation as
 $ \dfrac{\text{speed of first train}}{\text{speed of second train}}=\dfrac{7}{10} $
So, we get
 $ \dfrac{v}{u}=\dfrac{7}{10}................(iii) $
Now, put the value of u from the equation (ii) to the equation (iii). Hence, we get
 $ \dfrac{v}{100}=\dfrac{7}{10} $
On cross-multiplying the above equation we get
 $ v=\dfrac{100\times 7}{10}=\text{70km/hr} $
Hence, answer is 70km/hr

Note: Another approach for this question would be that we can suppose the speed of both the trains as 7x and 10x respectively from the ratio of speed 7:10. Now, we get 10x = 100 as both are the speed of the second train. Hence, get ‘x’ from the above equation and find the speed of the first train by calculating the value of 7x. One may go wrong while using the relation,
 $ \text{speed}=\dfrac{\text{distance}}{\text{time}} $
He or she may apply identity as \[\text{time}=\text{distance}\times \text{speed}\] or \[\text{speed}=\text{distance}\times \text{time}\] which are wrong. So, be careful with this identity, otherwise the whole solution will go wrong.