Question : A vehicle is going at one-fourth of its usual speed and it takes an extra 45 minutes to reach its destination. It's usual time to cover the same distance is:
Option 1: 15 minutes
Option 2: 10 minutes
Option 3: 30 minutes
Option 4: 20 minutes
Correct Answer: 15 minutes
Solution : Given, A vehicle is going at one-fourth of its usual speed and it takes an extra 45 minutes to reach its destination. We know that, time × Speed = Distance Let the usual speed of the train and distance be 4S km/h and D km. $\frac14$ of its usual speed = $\frac{4S}{4}$ = S km/h Time to cover the distance = $\frac{D}{4S}$ hours 45 minutes = $\frac34$ hours According to the question, $\frac{D}{S}-\frac{D}{4S}=\frac34$ ⇒ $\frac{4 - 1}{4S} = \frac{3}{4D}$ ⇒ $\frac{3}{S} = \frac{3}{D}$ ⇒ $\frac{D}{S} = 1$ ⇒ $\frac{D}{4S}=\frac14$ = $\frac14$ hours = $\frac14 × 60$ = 15 minutes Hence, the correct answer is 15 minutes.
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