uptetd16p1 q91
- Option : A
- Explanation : (A) Let the normal speed of the bus be 'x' km/h to cover the distance of 300 km in time 't' h.
∴ Distance = speed × time
⇒ 300 = x × t
If speed increased by 5 km/h, then
speed = (x + 5) km/h
and time = (t - 2)h
Then, distance = (x + 5) (t - 2)
⇒ 300 =(x + 5)(t - 2)
⇒ 300 = xt - 2x + 5t - 10
⇒ 2x2 + 10x - 1500 = 0
⇒ x2 + 5x - 750 = 0
⇒ x2 + 30x - 25x - 750 = 0
⇒ x(x + 30) - 25 (x + 30) = 0
⇒ (x - 25)(x + 30) = 0
⇒ x = 25, -30
Hence, normal speed of the bus is 25km/h
