A person cycles from hostel to college at a speed of 20 kmph and reaches 9.5 minutes late. If he cycles at a speed of 24 kmph and reaches early by 9.5 minutes, find the distance between hostel and college. (in km)

Let ideal time taken = $$t$$ hours

Also, speed is inversely proportional to time.

=> $$\frac{20}{24}=\frac{t-\frac{9.5}{60}}{t+\frac{9.5}{60}}$$

=> $$5t+\frac{9.5}{12}=6t-\frac{9.5}{10}$$

=> $$6t-5t=\frac{9.5}{12}+\frac{9.5}{10}$$

=> $$t=\frac{47.5+57}{60}=\frac{104.5}{60}$$

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

= $$20\times(\frac{104.5}{60}+\frac{9.5}{60})$$

= $$\frac{114}{3}=38$$ km

=> Ans - (C)