In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

Let speed of Ashok be denoted as $$S_A$$, speed of Bipin be denoted by $$S_B$$, speed of Chandan be denoted by $$S_C$$.

Also let Ashok takes $$t$$ seconds to complete the race.

So, $$\dfrac{S_A}{S_B}=\dfrac{t+15}{t}$$ ------>(1)

Also, $$\dfrac{S_A}{S_C}=\dfrac{t+25}{t}$$ ------>(2)

Also, it is given, Ashok beats Bipin by 150 metres.

So, $$\dfrac{S_A}{S_B}=\dfrac{400}{400-150}=\dfrac{400}{250}=\dfrac{8}{5}$$ ------>(3)

From equation (1) and (3),

$$\dfrac{t+15}{t}=\dfrac{8}{5}$$

or, $$5t+75=8t$$

or, $$3t=75$$

or, $$t=25$$

Dividing equation (2) by equation (1),

$$\dfrac{S_B}{S_C}=\dfrac{t+25}{t+15}=\dfrac{25+25}{25+15}=\dfrac{50}{40}=\dfrac{5}{4}=\dfrac{400}{320}$$

So, by the time Bipin has covered 400 metres (completed the race), C covers 320 metres.

So, Bipin beats Chandan by (400-320) metres = 80 metres