A truck covers a distance of 480 km at a certain speed. If the speed is decreased by 8km/h, it would have taken 2 hours more to cover the same distance, 50% of its original speed (in km) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer in option 3 i.e. 24
Let the speed of the truck be = x km/h
Hence;
480 km/(x - 8) - 480 km/x = 2 hours
⇒ 1/(x - 8) - 1/x = 2/480
⇒ x - x + 8/(x - 8)x = 1/240
⇒ 8 × 240 = x2 - 8x
⇒ x2 - 8x - 1920 =0
⇒ x2 + 40x - 48x - 1920 = 0
⇒ x(x + 40) - 48(x + 40) = 0
⇒ x = 48 since speed cant be a negative value
50% of the original speed = 48 × 1/2 = 24 km/h