Question : A car can cover a certain distance in $4\frac{1}{2}$ hours. If the speed increases by 5 km/hr, it would take $\frac{1}{2}$ hour less to cover the same distance. Find the slower speed of the car.
Option 1: 50 km/hr
Option 2: 40 km/hr
Option 3: 45 km/hr
Option 4: 60 km/hr
Correct Answer: 40 km/hr
Solution :
Ratio of time = $\frac{9}{2}:(\frac{9}{2}-\frac{1}{2})=\frac{9}{2}:4=9:8$
Ratio of speed = 8 : 9
Let the slower speed be 8k and the increased speed be 9k.
The speed of the car increased by 5 km/hr.
So, 9k – 8k = 5
⇒ k = 5
$\therefore$ Slower speed of car = 8 × 5 = 40 km/hr
Hence, the correct answer is 40 km/hr.
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