# Bholu is going Lucknow from his village Kharagpur by Bullet(bike). The Bullet covers first 75 km with a certain speed and next 90 km at an average spe

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Bholu is going Lucknow from his village Kharagpur by Bullet(bike). The Bullet covers first 75 km with a certain speed and next 90 km at an average speed of 10 km/hr more than the first speed. He reaches Lucknow in 3 hours. Find the original speed of Bullet.
1. 60 km/hr
2. 65 km/hr
3. 50 km/hr
4. 55 km/hr

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Correct Answer - Option 3 : 50 km/hr

Given∶

Total time taken to complete the journey = 3 hours

First 75 km covers with certain speed.

Next 90 km covers with average speed of 10 km/hr more than the first speed.

Formula used∶

Time = Distance/Speed

Calculation∶

Let the original speed of Bullet be x km/hr.

Time taken to over 75 km = 75 /x hours

New speed = (x + 10) km/hr.

Taken to cover 90 km with new speed = 90/(x + 10) hours.

Total time taken to cover the journey = 3 hours

∴ (75/x) + [90/(x + 10)] = 3

After solving this, we get

3x2 – 135x – 750 = 0

⇒ x2 – 45x – 250 = 0

⇒ x2 – 50x + 5x – 250 = 0

⇒ x(x – 50) + 5(x – 50) = 0

⇒ (x – 50) (x + 5) = 0

⇒ x – 50 = 0 or x + 5 = 0

⇒ x = 50 or x = - 5, which is not possible as speed cannot be negative.

∴ The original speed of the Bullet is 50 km/hr.