Question 87

A person cycles from hostel to college at a speed of 10 kmph and reaches 7 minutes late. If he cycles at a speed of 12 kmph, he reaches early by 6 minutes. Find the distance between hostel and college.

Solution

Let ideal time taken = $$t$$ hours

Also, speed is inversely proportional to time.

=> $$\frac{10}{12}=\frac{t-\frac{6}{60}}{t+\frac{7}{60}}$$

=> $$10t+\frac{7}{6}=12t-\frac{6}{5}$$

=> $$12t-10t=\frac{7}{6}+\frac{6}{5}$$

=> $$t=\frac{35+36}{60}=\frac{71}{60}$$

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

= $$10\times(\frac{71}{60}+\frac{7}{60})$$

= $$\frac{78}{6}=13$$ km

=> Ans - (A)

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