Total number of days taken to complete the task if after certain days one person leaves

Namachila November 19, 2025

0 0 2 minutes read

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:

Input: a = 10, b = 20, n = 5
Output: 10

Input: a = 5, b = 15, n = 3
Output: 6

Approach: Let D be the total number of days to complete the work. A and B work together for D – n days. So,

(D – n) * (1/a + 1/b) + (n) * (1/b) = 1
D * (1/a + 1/b) – (n/a) – (n/b) + (n/b) = 1
D * (1/a + 1/b) = (n + a) / a
D = b * (n + a) / (a + b)

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the
// number of days required
int numberOfDays(int a, int b, int n)
{
    int Days = b * (n + a) / (a + b);
 
    return Days;
}
 
// Driver code
int main()
{
    int a = 10, b = 20, n = 5;
 
    cout << numberOfDays(a, b, n);
 
    return 0;
}

Java

// Java implementation of the approach
import java.io.*;
 
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 (String[] args) 
{
 
    int a = 10, b = 20, n = 5;
    System.out.println (numberOfDays(a, b, n));
 
}
}
 
// This code is contributed by jit_t

Python3

# Python3 implementation of the approach
  
# Function to return the
# number of days required
def numberOfDays(a, b, n):
 
    Days = b * (n + a) // (a + b)
  
    return Days
 
# Driver code
if __name__ == "__main__" :
 
    a = 10
    b = 20
    n = 5
  
    print(numberOfDays(a, b, n))
 
# This code is contributed by rrrtnx

C#

// C# implementation of the approach 
using System;
 
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)); 
     
    } 
}
 
// This code is contributed by AnkitRai01

Javascript

<script>
// javascript implementation of the approach
 
    // Function to return the
    // number of days required
    function numberOfDays(a , b , n)
    {
        var Days = b * (n + a) / (a + b);
        return Days;
    }
 
    // Driver code
    var a = 10, b = 20, n = 5;
    document.write(numberOfDays(a, b, n));
 
// This code is contributed by Rajput-Ji
</script>

Output:

Time Complexity: O(1), since there is only basic arithmetic operation.

Auxiliary Space: O(1), since no extra space has been taken.

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!