​A man travels 360 km in 4 h, partly by air and partly by train. If he had travelled all the way by air, he would have saved $$\frac{4}{5}$$​ of the time he travelled by train, and he would have arrived at his destination 2 h early. Find the distance he travelled by air.​

Correct option is A

Given:

Total distance = 360 km

Total time = 4 h

If travelled entirely by air, he would have saved $$\frac{4}{5}$$​ of train time

He would also arrive 2 hours earlier if entirely by air

Formula Used:

Speed = $$\frac{Distance}{Time}$$​​

Solution:
Let distance travelled by air = x km
Then distance by train = 360 - x km
Let speed of air = A, and train = B

Let time taken by train = t, then time by air = 4 – t
If entire journey was by air, he would save $$\frac{4}{5} t$$​ and arrive 2 hours earlier. So:

​$$t - \frac{1}{5}t = 2 \\ \ \\ \implies \frac{4}{5}t = 2\\ \ \\ \implies t = 2.5 h$$​​

Then, time by air = 4 - 2.5 = 1.5 h

Now, 

Speed of train  = $$\frac{360 - x}{2.5}$$​​
Speed of air = $$\frac{x}{1.5}$$​​

Now, if travelled entire 360 km by air at $$\frac{x}{1.5},$$​​

total time = $$\frac{360}{\frac{x}{1.5}} = \frac{360 \times 1.5}{x}$$​​

So original time – air-only time = 2 hours:

​$$4 - \frac{360 \times 1.5}{x} = 2\\ \ \\ \frac{360 \times 1.5}{x} = 2 \\ \ \\ \frac{540}{x} = 2 \\ \ \\ x = 270$$​​

The distance travelled by air is 270 km