CAT 2020 Slot 1 QA Question 22: Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so a

Question

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so a

Accepted Answer

Let the distance from home to office be $D$ km. The difference between the two arrival times is 35 minutes, or $\dfrac{7}{12}$ hours.

$\dfrac{D}{8} - \dfrac{D}{15} = \dfrac{7}{12}$
$\Rightarrow \dfrac{7D}{120} = \dfrac{7}{12}$
$\Rightarrow D = 10$

From 9:10 am to 10:00 am, Amal has 50 minutes, or

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10:00 am?