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

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 `# Python 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 ` ` `  `a ``=` `10` `b ``=` `20` `n ``=` `5` ` `  `print``(numberOfDays(a, b, n)) ` ` `  `# This code is contributed by ihritik     `

## 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 `

Output:

```10
```

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Improved By : jit_t, AnkitRai01, ihritik