Correct Answer - Option 4 : 70 km

**Given:**

Rajesh covers 140 km in 15 hours to reach office from home.

The speed of bus is 14 km/hr.

The speed of cycle is 7 km/hr.

**Formula Used:**

Time = Distance/Speed

**Calculation:**

Rajesh covers 140 km in 15 hours to reach office from home.

The total time taken = 140/15 = 28/3 hours

Let the distance covered by bus be x.

The time taken by bus = x/14

The distance covered by cycle = 140 - x

The time taken by cycle = (140 - x)/7

The total time taken = x/14 + (140 - x)/7

⇒ x/14 + (140 - x)/7 = 15

⇒ x + 140 × 2 - 2x = 15 × 14

⇒ x = 280 - 210 = 70 km

The distance covered by cycle = 140 - 70 = 70 km

**∴ The distance covered by cycle is 70 km.**