Question

Let us assume a circular path. If a girl named Sonia can drive her car in $ 18 $ minutes and his friend Ravi can drive her car in $ 12 $ minutes. If they both started at the same time and the point of the circular path in the same direction. What is the time needed for them to meet at the same starting point?

Answer 1

Hint: This is a nice arithmetic problem. We can do this type of problem without using any mathematical concepts. We only need to know about the numbers to solve this problem. At first, we will find the time taken by each participant to take \[x,y\] rounds completely respectively and then equate them since they should meet at the starting point. After that, we try to find the \[x,y\] by using some logic.

Complete step-by-step answer:
Given that,
Sonia needs $ 18 $ minutes for a complete round,
Ravi needs $ 12 $ minutes for a complete round.
Let us look at the diagram for a clear idea.

Here, C is the center of the circle and S is the starting point of the circular path.
Now we can clearly say that,
Time taken for Sonia to complete $ x $ rounds in the circular path is \[18x\] ,
Time taken for Ravi to complete $ y $ rounds in the circular path is $ 12y $ .
They meet at the starting point and the total time they drive is the same.
Let us say Sonia took $ x $ rounds before they met and Ravi took $ y $ rounds.
It gives us,
 $ 18x = 12y, $
 $ \Rightarrow 3x = 2y $ .
Now we need to find $ x $ or $ y $ to find the required time.
Look at the equation $ 3x = 2y $ ,
We know that $ 3 $ does not divide $ 2 $
So, $ y $ must be divisible $ 3 $
The smallest positive number divisible by $ 3 $ is $ 3 $ .
So, $ y = 3 $
 $ \Rightarrow x = 2 $
And, Time required $ = 18x = 12y = 36 $ minutes.
Therefore the time required is $ 36 $ minutes.
So, the correct answer is “$ 36 $ minutes”.

Note: This is a nice problem to ask. The answer we got is the first time they meet after the start. They meet a lot of times after the first time. $ 36 $ minutes is the least time required for them to meet. We have to practice this type of problem before the exam because the idea of solving this question is not spontaneous.