Question 102
A person can board a bicycle for 20 km at the hotel. He travels at speeds 7.5 minutes late. If he had traveled at speeds of 24 km at 7.5 minutes earlier. Find the distance between the hotel and the college. (Km)
Solution
Let ideal time taken = $$t$$ hours
Also, speed is inversely proportional to time.
=> $$\frac{20}{24}=\frac{t-\frac{7.5}{60}}{t+\frac{7.5}{60}}$$
=> $$5t+\frac{7.5}{12}=6t-\frac{7.5}{10}$$
=> $$6t-5t=\frac{7.5}{12}+\frac{7.5}{10}$$
=> $$t=\frac{37.5+45}{60}=\frac{82.5}{60}$$
$$\therefore$$ Distance = speed $$\times$$ time
= $$20\times(\frac{82.5}{60}+\frac{7.5}{60})$$
= $$\frac{90}{3}=30$$ km
=> Ans - (B)
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