# Two people are cycling at the speed of 10.8 km/h and 12 km/h, a bus running in the same direction crosses the cyclist in 9 seconds and 13.5 seconds re

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Two people are cycling at the speed of 10.8 km/h and 12 km/h, a bus running in the same direction crosses the cyclist in 9 seconds and 13.5 seconds respectively. What is the length of the bus?

1. 11 m
2. 8 m
3. 9 m
4. 10 m

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Correct Answer - Option 3 : 9 m

Given:

Two people are cycling at a speed of 10.8 km/hr and 12 km/hr, and in the same direction, a bus is also traveling. The bus crosses two people in 9 and 13.5 seconds.

Formula used:

Speed = Distance/ Time

Calculation:

Let us assume the speed of the Bus = B km/hr, L m be the length of the bus.

Now the distance traveled by two people while Bus crosses them is the length of the Bus.

⇒ (L) m = (B – 10.8) × 9 × 5/18 = (B – 12) × 13.5 × 5/18

⇒ (B – 10.8) × 9 = (B – 12)× 13.5

⇒ 2× (B – 10.8) = 3× (B – 12)

⇒ 2B – 21.6 = 3B – 36

⇒ 36 – 21.6 = 3B – 2B

⇒ B = 14.4 Km/hr

Now the length of the bus L m will be

∴  (14.4 – 12) × 13.5 × 5/18 = 9 m