Question

Starting from his house in village A, a person has to reach

another village B to attend a function just in time. If he

plans to cycle at the speed of 8 km/hr, he would reach late

by 15 minutes. But if he plans to cycle at a speed of

10 km/hr, he would reach earlier by 15 minutes. The

distance between the two villages is
Ans-20 km​

Answer 1

The man reaches 15 minutes late with 8 km/hr speed and 15 minutes early with a speed of 10 km/hr then the distance between the two villages A and B is 20 km.

Step-by-step explanation:

Let the distance between the two villages A & B be “d” km.

The time taken to cover the distance d if he cycles at a speed of 8 km/hr = $\frac{d}{8}$ hr

The time taken to cover the distance d if he cycles at a speed of 10 km/hr = $\frac{d}{10}$ hr

According to the question,

The difference between time of the two journeys = 15 + 15 = 30 minutes = $\frac{30}{60}$ hr.

Now, the final equation will be,

$\frac{d}{8}$ - $\frac{d}{10}$ = $\frac{30}{60}$

⇒ d $\frac{10-8}{80}$ = ½  

⇒ d = $\frac{80}{2*2}$

⇒ d = 20 km

Thus, the distance between the two villages is 20 km.

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