# Rajesh covers 140 km in 15 hours to reach office from home. He covers some distance by bus with a speed of 14 km/hr and rest part of distance by cycle

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Rajesh covers 140 km in 15 hours to reach office from home. He covers some distance by bus with a speed of 14 km/hr and rest part of distance by cycle with the speed of 7 km/hr. What distance he covered by cycle?

1. 60 km
2. 50 km
3. 55 km
4. 70 km
5. 65 km

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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.