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Shantanu drives a motorcycle and covers a distance of 715 km at a constant speed.
If the speed of the motorcycle had been 10 km/h more, he would have taken 2 h less to cover the same distance. What is the original speed of the motorcycle?
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- 65 km/h
- 55 km/h
- 60 km/h
- 36 km/h
Correct Option: B
Let the constant speed = V
According to the question,
715/V - 715/(V + 10) = 2
⇒ 1/V - 1/(V + 10) = 2/715
⇒ [(V + 10) - V] / [V(V + 10)] = 2/715
⇒ V2 + 10V = 10 x 715/2
⇒ V2 + 10V - 3575 = 0
⇒ V2 + 65V - 55V - 3575 = 0
⇒ V(V + 65) - 55(V + 65) = 0
⇒ (V - 55) (V + 65) = 0
∴ V = 55 or V = - 65
Ignoring the negative value, we get V = 55
∴ Original speed of the motorcycle = 55 km/h
