Aravind and Biswanath start at the same time from their hostel and go to the ground with speeds of 30 km/h and 60 km/h, respectively. If Aravind takes 20 minutes longer than Biswanath to reach the ground, then find the distance between their hostel and the
ground.

Given:

Aravind's speed = 30 km/h

Biswanath's speed = 60 km/h

Aravind takes 20 minutes longer than Biswanath

Concept:

Time = Distance / Speed

Formula Used:

Let the distance between their hostel and the ground be $d$ km.

Time taken by Aravind = $\frac{d}{30}$ hours

Time taken by Biswanath = $\frac{d}{60}$ hours

Given that Aravind takes 20 minutes (which is $\frac{1}{3}$ hours) longer than Biswanath:

$\frac{d}{30} = \frac{d}{60} + \frac{1}{3}$

Calculation:

We have,

$\Rightarrow \frac{d}{30} = \frac{d}{60} + \frac{1}{3}$

$\Rightarrow \frac{d}{30} - \frac{d}{60} = \frac{1}{3}$

$\Rightarrow \frac{2d - d}{60} = \frac{1}{3}$

$\Rightarrow \frac{d}{60} = \frac{1}{3}$

$\Rightarrow d = 60 \times \frac{1}{3}$

$\Rightarrow d = 20$ km

∴ The distance between their hostel and the ground is 20 km.