Question

Ram is cycling. To reach, his destination he has to cover a distance of 9 km. He covers first 4 km with a certain speed and then he increases the speed by 3 km of twice of original speed to cover the next 5 km, by doing this he reached 3 hours earlier at his destination. Find the original speed of the cycle.
1. 7 km/hr
2. 5 km/hr
3. 3 km/hr
4. 1 km/hr

Answer 1

Correct Answer - Option 4 : 1 km/hr

Given∶

Ram covers first 4 km with a certain speed.

Then he increases the speed by 3 km of twice of original speed to cover the next 5 km, by doing this he reached 3 hours’ earlier.

Formula Used∶

Concept of Quadratic equation, Time = Distance / Speed

Calculation∶

Let the original speed of the cycle be x km/hr. Then

Time taken to cover first 4 km = 4/x hours

Time taken to next 5 km when he increase the speed by 3 km of twice of original speed = 5/(2x+ 3)

It is given that, the time to cover total distance is reduced by 3 hours.

 (4/x) – 5/(2x + 3) = 3

⇒ 4/x – 3 = 5/(2x + 3)

⇒ (4 – 3x)/x = 5/(2x + 3)

⇒ (4 – 3x) (2x + 3) = 5x

⇒ 6x² + 6x – 12 = 0

⇒ x² + x – 2 = 0

⇒ x² + 2x – x – 2 = 0

⇒ x(x + 2) – 1(x + 2) = 0

⇒ (x – 1) (x + 2) = 0

⇒ x – 1 = 0 or x + 2 = 0

⇒ x = 1 or x = - 2, ignore if as speed cannot be negative.

∴ The original speed of the cycle is 1 km/hr.