Given that person A takes a days to do a certain piece of work while person B takes b days to do the same work. If A and B started the work together and n days before the completion of work, A leaves the work. Find the total number of days taken to complete work.
Examples:Â
Input: a = 10, b = 20, n = 5Â
Output: 10Input: a = 5, b = 15, n = 3Â
Output: 6Â Â
Approach: Let D be the total number of days to complete the work. A and B work together for D – n days. So, Â
(D – n) * (1/a + 1/b) + (n) * (1/b) = 1Â
D * (1/a + 1/b) – (n/a) – (n/b) + (n/b) = 1Â
D * (1/a + 1/b) = (n + a) / aÂ
D = b * (n + a) / (a + b)Â
Below is the implementation of the above approach:Â
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;Â
// Function to return the// number of days requiredint numberOfDays(int a, int b, int n){Â Â Â Â int Days = b * (n + a) / (a + b);Â
    return Days;}Â
// Driver codeint main(){Â Â Â Â int a = 10, b = 20, n = 5;Â
    cout << numberOfDays(a, b, n);Â
    return 0;} |
Java
// Java implementation of the approachimport java.io.*;Â
class GFG {Â Â Â Â Â // Function to return the// number of days requiredstatic int numberOfDays(int a, int b, int n){Â Â Â Â int Days = b * (n + a) / (a + b);Â
    return Days;}Â
// Driver codepublic static void main (String[] args) {Â
    int a = 10, b = 20, n = 5;    System.out.println (numberOfDays(a, b, n));Â
}}Â
// This code is contributed by jit_t |
Python3
# Python3 implementation of the approach  # Function to return the# number of days requireddef numberOfDays(a, b, n):Â
    Days = b * (n + a) // (a + b)      return DaysÂ
# Driver codeif __name__ == "__main__" :Â
    a = 10    b = 20    n = 5      print(numberOfDays(a, b, n))Â
# This code is contributed by rrrtnx |
C#
// C# implementation of the approach using System;Â
class GFG {          // Function to return the     // number of days required     static int numberOfDays(int a, int b, int n)     {         int Days = b * (n + a) / (a + b);              return Days;     }          // Driver code     public static void Main ()     {              int a = 10, b = 20, n = 5;         Console.WriteLine(numberOfDays(a, b, n));          } }Â
// This code is contributed by AnkitRai01 |
Javascript
<script>// javascript implementation of the approachÂ
    // Function to return the    // number of days required    function numberOfDays(a , b , n)    {        var Days = b * (n + a) / (a + b);        return Days;    }Â
    // Driver code    var a = 10, b = 20, n = 5;    document.write(numberOfDays(a, b, n));Â
// This code is contributed by Rajput-Ji</script> |
10
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Time Complexity: O(1), since there is only basic arithmetic operation.
Auxiliary Space: O(1), since no extra space has been taken.
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