Given three integers A, B, and C, the task is to find the length of a race track if 3 racers are competing in a race where the first racer beats the second racer by A meters, the first racer beats the third racer by B meters and the second racer beats the third by C meters.
Examples:
Input: A = 11, B = 90, C = 80
Output: 880Input: A = 10, B = 20, C = 12
Output: 60
Approach :
Let X be the length of the race track.
Case 1: By the time when the First racer finished the race, the distances covered by all the 3 racers are:
First = X, Second = X – A, Third = X – B
Let the time taken by the First racer to finish the race be T1.
Case 2: By the time when the Second racer finished the race, the distances covered by the remaining 2 racers are:
Second = X, Third = X – C
Let the time taken by the Second racer to finish the race be T2.
The ratio of the speeds of the Second and the Third racer will be constant in both case 1 and case 2 which implies:
=> ((X – A) / T1) / ((X – B) / T1) = (X / T2) / ((X – C) / T2)
=> (X – A) / (X – B) = (X) / (X – C)
=> X2 – A*X – C*X + A*C = X2 – B*X
=> A*C = (C + A – B)*X
=> X = A*C / (C + A – B)
Below is the implementation of the above program:
C++
// C++ Program for the above approach#include <bits/stdc++.h>using namespace std;#define int long longint32_t main(){ int A = 11; int B = 90; int C = 80; int ans = C * A; ans = ans / (C + A - B); cout << ans << endl;} |
Java
// Java Program for the// above approachimport java.util.Scanner;class GFG { public static void main(String args[]) { int a = 11; int b = 90; int c = 80; System.out.println(c * a / (c + a - b)); }} |
Python3
# Python3 Program for the # above approach # Function to get the length# of the race trackdef findlength(a, b, c): # return the answer return c * a/(c + a-b)a = 11b = 90c = 80print(findlength(a, b, c)) |
C#
// C# program for the above approach using System;class GFG{ static void Main(){ int a = 11; int b = 90; int c = 80; Console.WriteLine(c * a / (c + a - b));}}// This code is contributed by divyeshrabadiya07 |
Javascript
<script>// JavaScript program for the above approach // Driver Codelet a = 11;let b = 90;let c = 80;document.write(c * a / (c + a - b));// This code is contributed by sanjoy_62 </script> |
880
Time Complexity: O(1)
Auxiliary Space: O(1)
Note: This is an interview question asked at POSTMAN (SDE Internship)
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