Question

A marathon track has a total length equal to $50km$. The start and end point of the track is P and Q respectively. Amit and Bhavesh started running from point P at the same time to reach point Q. Amit takes two hours more than Bhavesh to reach Q. Also, Amit reaches the mid-point of P and Q one hours before Bhavesh reaches Q. The speed of Bhavesh, in km per hour is

• A. $15$
• B. $12.5$
• C. $14.5$
• D. $18$

Answer 1

Answer: (B)

$12.5$

Let $t_B$ & $t_A$ be the total time taken by Bhavesh and Amit to reach at point Q respectively.

Let $V_A$ & $V_B$ be the speeds of Amit and Bhavesh respectively in km per hour.

$\to$ According to the given condition.

$t_A-2=t_B$

$\frac{50}{V_A}-2=\frac{50}{V_B}$
$50(\frac{1}{V_A}-\frac{1}{V_B})=2$

$\frac{1}{V_A}-\frac{1}{V_B}=\frac{1}{25}$ ................(i)

$\to$ Also, it is known that Amit reaches mid point of P & Q one hour before Bhavesh reaches Q.

$\frac{50}{V_B}-1=\frac{25}{V_A}$

$25(\frac{2}{V_B}-\frac{1}{V_A})=1$

$\therefore \frac{2}{V_B}-\frac{1}{V_A}=\frac{1}{25}$ .................(ii)

Add eq. (i) and eq. (ii)

$\frac{1}{V_B}=\frac{2}{25}$

$\therefore V_B=12.5\text{km / hr}$