The table given below shows the data about track record of car racing game, where 4 cars P, Q, R and S are competing to reach finishing line which is at a distance of 3000 m from their initial starting point.

1. Drift refers to over starting intentionally done by driver.
2. While calculating average speed, do not consider time taken in drift/crash.
3. Points = 50 × drifts – 20 × crashed

Cars	Drift	Time to reach finishing line (in sec)	Crash
P	5	180	3
Q	7	120	5
R	6	150	4
S	8	100	6

How much speed does car R need to gain in order to cover twice the distance in  $\frac{5}{3}$ of the original time taken?  

The correct answer is 24 m/s.

We can solve this problem step-by-step by calculating the new distance and the new time limit for car R, and then determining the required speed:

Step 1: Identify the original values for car R from the table and description
- The finishing line distance (original distance) = 3000 m
- The original time taken by car R = 150 seconds

Step 2: Calculate the new distance to be covered
The question states that car R needs to cover twice the original distance:
New Distance = 2 × 3000 m = 6000 m

Step 3: Calculate the new time limit
The new time limit is 5/3 of the original time taken:

$\text{New Time}=\frac{5}{3}\times 150\text{seconds}=250\text{seconds}$

Step 4: Calculate the required speed
Using the formula for speed:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Substitute the new distance and new time into the formula:

$\text{Required Speed}=\frac{6000}{250}=24\text{m/s}$

Therefore, the speed car R needs to reach is 24 m/s.