Question : A car starts from point A towards point B, travelling at the speed of 20 km/hr. $1\frac{1}{2}$ hours later, another car starts from the point and travels at the speed of 30 km/hr and reaches $2\frac{1}{2}$ hours before the first car. Find the distance between A and B.
Option 1: 300 km
Option 2: 240 km
Option 3: 260 km
Option 4: 280 km
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Correct Answer: 240 km
Solution :
Let the time taken by the first car to reach point B be $t$ hours.
The time taken by the second car to reach point B = $t - 1\frac{1}{2} - 2\frac{1}{2} = t - 4$ hours
Since the distance travelled is the same for both cars.
Distance = Speed × Time
So, for the first car, the distance is $20t$ and for the second car, the distance is $30(t - 4)$.
$⇒20t = 30(t - 4)$
$\therefore t = 12$
This is the time taken by the first car to reach point B.
So, the distance between points A and B = Speed × Time = 20 × 12 = 240 km
Hence, the correct answer is 240 km.
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