Question : A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/hr speed and 10 minutes earlier if he walks at a speed of 4 km/hr. The distance he has to walk is:
Option 1: 24 km
Option 2: 12.5 km
Option 3: 10 km
Option 4: 6 km
Correct Answer: 6 km
Solution :
Let $x$ be the required distance.
Time taken in the first case = $\frac{x}{3}$ hours
Time taken in the second case = $\frac{x}{4}$ hours
Time difference = $\frac{x}{3} - \frac{x}{4}$ hours
So, $\frac{x}{3} - \frac{x}{4}$ = $\frac{(20+10)}{60}$
⇒ $\frac{x}{12}$ = $\frac{1}{2}$
⇒ $x$ = 6 km
Hence, the correct answer is 6 km.
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