Question

In crossing a distance of $30$km. A takes $2$hrs more than B. If A double his speed , he wo have taken $1$ hr less than B. Then trir speeds are

• A. $5$ km/hr and $7.5$ km/hr
• B. $5.5$ km/hr and $7.5$ km/hr
• C. $4.5$ km/hr and $5.5$ km/hr
• D. none of these

Answer 1

The correct option is A $5$ km/hr and $7.5$ km/hr

The distance is 30 Km.

First, A takes 2 hrs more then B.

Let, $S_A$ be the speed of A and S be the speed of B .

We know, distance = speed X time

$\Rightarrow \text{time}=\frac{\text{Distance}}{\text{Speed}}$

$\therefore$ According to the question,

$\frac{30}{S_A}-\frac{30}{S}=2$

$\Rightarrow \frac{30}{S}=\frac{30}{S_A}-2$ ----eq.1

Secondly, when speed of A is doubled it becomes $2S_A$ and the difference of time is 1 hour .

$\therefore$ According to the question.

$\frac{30}{S}-\frac{30}{2S_A}=1$

$\Rightarrow \frac{30}{S}=1+\frac{30}{2S_A}$ ----eq.2

Form eq.1 & eq.2 we have,

$\frac{30}{S_A}-2=1+\frac{30}{2S_A}$

$\Rightarrow \frac{30}{2S_A}=3\Rightarrow S_A=5km/hr$

$\therefore$ putting the value of $S_A=5$ in eq.1 , we have, S = 7.5 km/hr.

$\therefore$ option A is correct.