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).
Answer & explanation
Correct answer: option 2
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