The road by which a car travels from city ‘E’ to city ‘F’ consists of uphill journey, downhill journey and journey on the flat surface. Time taken by the car while going from city ‘E’ to ‘F’ is 5 hours while it took 5 hours and 50 minutes to travel from city ‘F’ to ‘E’ via the same path. If average speed of the car in uphill, downhill and on flat surface was 20 km/h, 30 km/h and 24 km/h, respectively, then find the distance between city ‘E’ and ‘F’?

Let total distance between city ‘E’ and ‘F’ = ‘d’ km And, distance travelled in uphill and downhill is ‘x’ km and ‘y’ km, respectively So, (x / 20) + (y / 30) + (d - (x + y)) / 24 = 5 --- (I) And, (y / 20) + (x / 30) + (d - (x + y)) / 24 = 35 / 6 --- (II) By adding equation (I) and equation (II), we get (x + y) * (1 / 20 + 1 / 30) + 2 * (d - (x + y)) / 24 = 5 + 35 / 6 Or, (x + y) * (5 / 60) + (d - (x + y)) / 12 = 65 / 6 Or, (x + y) / 12 + (d - (x + y)) / 12 = 65 / 6 Or, d / 12 = 65 / 6 So, d = 130 Therefore, distance between city ‘E’ and city ‘F’ = 130 km Hence, the correct answer is C.