Question

A person covers a distance of 300 km and then returns to the starting point. The time taken by him for the outward journey is 5 hours more than time taken for the return journey. If he returned at a speed of 10 km/h more than the speed of going. What was the speed (in km/h) for the outward journey?
1. 15 km/h
2. 20 km/h
3. 30 km/h
4. 25 km/h

Answer 1

Correct Answer - Option 2 : 20 km/h

Given:

Distance covered by the person in a single journey = 300km

Time taken by him for the outward journey = 5 hours more than the time taken for the return journey.

The return speed is 10km/h more than the speed of going.

Formula used:

Distance covered = Speed × Time taken

Calculation:

Let the speed of outward journey be ‘x’ km/h

Hence, the speed of return journey will be (x + 10) km/h

So, time taken in return journey = 300/(x + 10) hours

Time taken in outward journey = (300/x) hours

According to the question,

⇒ (300/x) – 300/(x + 10) = 5

⇒ [300(x + 10) – 300x]/x(x + 10) = 5

⇒ [300x + 3000 – 300x] = 5x(x + 10)

⇒ 3000 = 5x² + 50x

⇒ 5x² + 50x – 3000 = 0

⇒ x² + 10x – 600 = 0

⇒ x² + 30x – 20x – 600 = 0

⇒ x(x + 30) – 20(x + 30) = 0

⇒ (x – 20)(x + 30) = 0

⇒ x = 20, -30

⇒ x = 20km/h as negative speed is not possible.

∴ The speed for the outward journey is 20km/h