​Ram covers a certain distance on a toy train. Had the train moved 8 km/h faster, it would have taken 20 min less. If it had moved 4 km/h slower, it would have taken 40 min more. Find the distance.​

Correct option is B

Given

If the speed increases by 8km/h, the time taken decreases by 20 min = $$\frac{1}{3}$$​​hours.

If the speed decreases by 4 km/h, the time taken increases by 40 min = $$\frac{2}{3}$$​ hours

Formula Used:

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

Solution: ​

Let the distance be d and speed be x 

then original time = $$\frac{d}{x}$$ ​

From condition 1; 

​$$\frac{d}x -\frac{d}{x+8} = \frac{1}{3} \\ \ \\ 24d = x^2+8x....(1)$$  

From condition 2;

​$$\frac{d}x -\frac{d}{x-4} = \frac{2}{3}\\ \ \\ -12d = 2x^2-8x\\ \ \\ -6d = x^2 - 4x$$....(2)

solving these two equation for d we get;

Distance (d)  = $$\frac{16}{3}$$​  km