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.