Question 89

A person cycles from hostel to college at a speed of 20 kmph and reaches 6.5 minutes late. If he cycles at a speed of 24 kmph and reaches early by 6.5 minutes, find the distance between hostel and college. (in km)

Solution

Let ideal time taken = $$t$$ hours

Also, speed is inversely proportional to time.

=> $$\frac{20}{24}=\frac{t-\frac{6.5}{60}}{t+\frac{6.5}{60}}$$

=> $$5t+\frac{6.5}{12}=6t-\frac{6.5}{10}$$

=> $$6t-5t=\frac{6.5}{12}+\frac{6.5}{10}$$

=> $$t=\frac{32.5+39}{60}=\frac{71.5}{60}$$

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

= $$20\times(\frac{71.5}{60}+\frac{6.5}{60})$$

= $$\frac{78}{3}=26$$ km

=> Ans - (C)

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