Places A and B are 20 km apart on the highway. A car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in one hour. If they travelled towards each other, they met in 12 minutes. What are the speeds (in km/h) of two cars?

Distance between place A and B = 20 km

If the cars travel in the same direction at different speeds, they meet in one hour.

If they travelled towards each other, they met in 12 minutes.

Speed = $$\frac{Distance}{Time}$$​​

Let the speed of first car be x km/h and second car be y km/h.

When they travel in same direction, relative speed = (x - y) km/h

Substituting the values, we get:

x - y = $$\frac{20}{1}$$​​

x - y = 20

x = y + 20   (Eq. 1)

When they travel in opposite direction, relative speed = (x + y) km/h

Substituting the values, we get

x + y = $$\frac{20}{\frac{12}{60}}=\frac{20\times 5}{1}=100$$​​

x = 100 - y  (Eq. 2)

Equating both the equations, we get

y + 20 = 100 - y

y + y = 100 - 20

2y = 80

y = $$\frac{80}{2}=40 km/h$$​​

x = 40 + 20 = 60 km/h 

Alternate Method: 

We can directly find the speed of the car by applying hit and trial method from the options:

Only option (A). 60 , 40  satisfies the equation (1) and (2). 

Thus, option(A) is the correct option.