Ravi and Rajiv decided to run a 960 m long race on a track as long as the length of the race.

Which of the statement(s) below is (are) sufficient to conclude that Rajiv ran at a speed of 10 m/s?

Statement 1: Rajiv gave Ravi an 80 m head start

Statement 2: Ravi ran at 8 m per second.

Statement 3: Rajiv caught up with Ravi with $$\frac{3}{8}$$​ of the track length still to be covered.

Correct option is D

Given:
The total race length is 960 meters.

Formula Used:

Distance = Speed $$\times$$ Time

Solution:
Statement 1: Rajiv gave Ravi an 80 m head start

Distance covered by Rajiv = 960 meters

Distance covered by Ravi = 960 - 80 =  880 meters

Statement 2: Ravi ran at 8 m per second.

Statement 3: Rajiv caught up with Ravi with $$\frac{3}{8}$$​  of the track length still to be covered.

Rajiv has covered 600 meters by the time Ravi has 360 meters left to run. From this, we can calculate the time it takes for Ravi to cover 520 meters.

(since Ravi has 360 meters left, so he must have run 520 meters).

Time taken by Ravi to cover 520 meters:

Time = $$\frac{520}{8}$$ = 65 meters

During this 65 seconds, Rajiv covers 600 meters. Therefore, Rajiv's speed is:

Speed of Rajiv = $$\frac{600}{65}$$ = 9.23 meter/second $$\ne 10 \text{ m/s}$$​​

This is not equal to 10 m/s, which contradicts the assumption that Rajiv's speed is 10 m/s.

Thus, the correct option is (d) Even all the three statements taken together is not sufficient.