Question 95

# A person cycles from hostel to college at a speed of 15 kmph and reaches 2.5 minutes late. If he cycles at a speed of 20 kmph and he reaches early by 2.5 minutes. Find the distance between hostel and college. (in KM)

Solution

Let ideal time taken = $$t$$ hours

Also, speed is inversely proportional to time.

=> $$\frac{15}{20}=\frac{t-\frac{2.5}{60}}{t+\frac{2.5}{60}}$$

=> $$15t+\frac{2.5}{4}=20t-\frac{2.5}{3}$$

=> $$20t-15t=\frac{2.5}{4}+\frac{2.5}{3}$$

=> $$t=\frac{7.5+10}{60}=\frac{17.5}{60}$$

$$\therefore$$ Distance = speed $$\times$$ time

= $$15\times(\frac{17.5}{60}+\frac{2.5}{60})$$

= $$\frac{20}{4}=5$$ km

=> Ans - (A)