Question

Rajat and Arif are jogging around a circular park. Arif jogs at half the speed of rajat and completes six rounds in 1 hour. If Rajat jogs 432 m in 12 minutes, then what is the perimeter of the park?
 $
  (a)\,120m \\
  (b)\,150m \\
  (c)\,180m \\
  (d)\,210m \\
 $

Answer 1

Hint: Find distance travelled in one hour and divide it by number of rounds in one hour.
First, we are going to find the speed of rajat from the given question and then from that we are going to find the speed of Arif, then we will find the distance travelled by Arif in one hour and then divide it with the number of rounds covered in 1 hour. Then, we will get the perimeter of the park.

Complete step by step solution:
First, we are going to find the speed of Rajat,
So, we are given rajat jogs 432 m in 12 minutes from which we get his speed
 $ Speed(rajat) = \dfrac{{432}}{{12}} = 36\,\,\,m/\min $
Since, we know that speed of Arif jogs half the speed of rajat, which is
 $ Speed(rajat) = \dfrac{{36\,}}{2}\,\,m/\min = 18\,\,m/\min $
Now, we will have to find the distance travelled in one hour, which is
 $ dis\tan ce = 18 \times 60 = 1080\;m $
So, we know that Arif completed 6 rounds in 1 hour, from which we can find the distance of each round which is the perimeter of the park.
 $ Perimeter = \dfrac{{1080}}{6} = 180\;m $

So, the correct answer is “Option C”.

Note: To solve this question, we should have good logical thinking as there is no need for perimeter formula as we have everything simplified in the question, which will get us the required answer and also, we need to know the relation between speed and distance.