Question

16. If time taken to travel between two stations has to be reduced by 20%, then by what per cent would the speed of the train has to be increased? (A) 15% (B) 20% (C) 25% (D) 30%​

Answer 1

Answer:

I think the answer should be 20%

Answer 2

For decreasing the travel time by 20%, the speed has to be increased by 25% (C).

Explanation:

Let the distance traveled by the person everyday be X.

and let the time taken to travel this distance (X) be T

Now,

According to the question,

We have assumed the distance to travel is X , The time taken is T

Hence,

The speed will be $S=\frac{X}{T}$

The time taken to travel has to be reduced by 20% of what the time now is required.

Therefore the new time (T') will be T - 20%T .

Hence,

$T' = T-\frac{20}{100} T\\ T' = \frac{80}{100}T \\T'= 0.8 T$

As we know, the distance to travel will remain the same

Hence,

The new speed (S') will be

$S' = \frac{X}{T'}$

Substituting the value of T' , we get

$S' = \frac{X}{0.8T}$

We can see that,

from (i)

$S'=\frac{5}{4} S$    

Hence, the speed % that is needed to be increase, will be

$= \frac{(S'-S)}{S}*100$

$= \frac{(\frac{5}{4}S )- S}{S}*100$  ;or

= 25%

Final Answer:

Hence, the speed that needs to be increased will be option (C) 25%.