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Question 98

If a man starts at A and walks at 5 kmph he will reach B late by 7 minutes. But if walks at 6 kmph he will reach B early by 5 minutes. The distance between A and B (in km) is

Solution

Let the distance between A and B be d km and the ideal time needed to reach the destination be t hours

Now, in the first case, we can say that $$\frac{d}{5}=t+\frac{7}{60}$$
That is $$t=\frac{d}{5}-\frac{7}{60}$$

Now, in second case, we can say that $$\frac{d}{6}=t-\frac{5}{60}$$
That is $$t=\frac{d}{6}+\frac{5}{60}$$

Equating both the sides for t, we get d = 6 km

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