Correct Answer - Option 3 : 40, 30
Given∶
Distance = 120 km
Average speed of car is 10 km more than the speed of bike.
A car takes 1 hour less than bike to cover the same distance.
Formula Used∶
Time = Distance/ Speed
Calculation∶
Let the speed of the bike be x km/hr
Then, the speed of the car be (x + 10) km/hr
According to question,
120/x – 120/(x + 10) = 1
⇒ [120(x + 10) – 120 x]/x(x + 10) = 1
⇒ 120x + 1200 – 120x = x2 + 10x
⇒ x2 + 10x – 1200 = 0
⇒ x2 + 40x – 30x – 1200 = 0
⇒ x (x + 40) – 30(x + 40) = 0
⇒ (x – 30) (x + 40) = 0
⇒ x - 30 = 0 or x + 40 = 0
⇒ x = 30 or x = - 40, which is not possible as speed is not negative.
So, bike’s speed = x = 30km/hr.
And car’s speed = x + 10 = 30 + 10 = 40 km/hr.
∴ The average speed of car is 40 km/hr and of bike is 30 km/hr.