A person has to cover 225 km distance. If he increases his speed by 5 km/h he reaches 1.5 hrs early. Find his initial speed (in km/hr).

25

Time = \(\frac{distanc}{speed}\)

Total distance = 225km

Let the initial speed = x km/hr

Increased speed = (x + 5) km/hr

ATQ,

⇒ \(\frac{225}{x}\) - \(\frac{225}{x\;+\;5}\) = 1.5 hrs

⇒ 225 (\(\frac{1}{x}\) - \(\frac{1}{x\;+\;5}\)) = \(\frac{3}{2}\)

⇒ 75 (\(\frac{5}{x(x\;+\;5)}\)) = \(\frac{1}{2}\)

⇒ x(x+5) = 750

Now, from option (b), we can easily justify the equation.

Therefore,

x = initial speed = 25 km/hr