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Total number of days taken to complete the task if after certain days one person leaves
• Last Updated : 13 Apr, 2021

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 ``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

 ``
Output:
`10`

Time Complexity: O(1 )

Auxiliary Space: O(1)

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