Question : The ratio of the speed of Aman, Kamal, and Manan is 2 : 3 : 4 respectively. What is the ratio of the time taken by Aman, Kamal, and Manan respectively to cover the same distance?
Option 1: 4 : 3 : 2
Option 2: 2 : 3 : 4
Option 3: 6 : 4 : 3
Option 4: 8 : 9 : 16
Correct Answer: 6 : 4 : 3
Solution :
If speed is inversely proportional to time, the ratio of time taken will be inverse to the ratio of the speed.
Given ratio = 2 : 3 : 4
Inverse of the given speed ratio = $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$
Taking the LCM of (2, 3, 4) = 12
Now multiplying the given ratio by 12, we get,
Inverse of the given speed ratio = $\frac{1}{2} \times 12 : \frac{1}{3} \times 12: \frac{1}{4}\times 12$
Inverse of the given speed ratio = 6 : 4 : 3
$\therefore$ the ratio of time taken by Aman, Kamal, and Manan is 6 : 4 : 3.
Hence, the correct answer is 6 : 4 : 3.
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