Question

A bike runs with the speed of 32 km/hr for (x + 5) hours, then with 25% more speed for (2x - 5) hours. If the distance covered in (x + 5) hours is 120 km more than the distance covered in (2x - 5) hours, then find the value of x.

1. 4
2. 3
3. 5
4. 7
5. 6

Answer 1

Correct Answer - Option 3 : 5

Given:

A bike speed for (x + 5) hours is 32 km/hr

Difference between distance covered in (x + 5) hours and (2x - 5) hours is 120 km

Formula used:

Speed = Distance / Time

⇒ Distance = Speed × Time

Calculation:

Distance covered in (x + 5) hours = 32 × (x + 5) = 32(x + 5)

Speed for (2x - 5) hours = 32 × (100 + 25) / 100 

⇒ 32 × 125 / 100 = 40 km/hr

Distance covered in (2x - 5) hours = 40 × (2x - 5) = 40(2x - 5)

According to question,

⇒ 32(x + 5) – 40(2x - 5) = 120

⇒ 32x + 160 – 80x +200 = 120

⇒ 360 – 48x = 120

⇒ 240 = 48x

⇒ x = 5

Hence, the value of x is 5