# Find the number which when added to the given ratio a : b, the ratio changes to c : d

Given four integers a, b, c and d. The task is to find the number X which when added to the numbers a and b the ratio changes from a : b to c : d.

Examples:

Input: a = 3, b = 6, c = 3, d = 4
Output: 6
When 6 is added to a and b
a = 3 + 6 = 9
b = 6 + 6 = 12
And, the new ratio will be 9 : 12 = 3 : 4

Input: a = 2, b = 3, c = 4, d = 5
Output: 2

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

Approach: Old ratio is a : b and new ratio is c : d. Let the required number be X,
So, (a + X) / (b + X) = c / d
or, ad + dx = bc + cx
or, x(d – c) = bc – ad
So, x = (bc – ad) / (d – c)

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the ` `// required number X ` `int` `getX(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``int` `X = (b * c - a * d) / (d - c); ` `    ``return` `X; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 2, b = 3, c = 4, d = 5; ` ` `  `    ``cout << getX(a, b, c, d); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to return the ` `// required number X ` `static` `int` `getX(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``int` `X = (b * c - a * d) / (d - c); ` `    ``return` `X; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `{ ` ` `  `    ``int` `a = ``2``, b = ``3``, c = ``4``, d = ``5``; ` `    ``System.out.println (getX(a, b, c, d)); ` ` `  `} ` `} ` ` `  `// The code is contributed by ajit..@23  `

## Python

 `# Python3 implementation of the approach ` ` `  `# Function to return the ` `# required number X ` `def` `getX(a, b, c, d): ` ` `  `    ``X ``=` `(b ``*` `c ``-` `a ``*` `d) ``/``/` `(d ``-` `c) ` `    ``return` `X ` ` `  `# Driver code ` ` `  `a ``=` `2` `b ``=` `3` `c ``=` `4` `d ``=` `5` ` `  `print``(getX(a, b, c, d)) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to return the ` `// required number X ` `static` `int` `getX(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``int` `X = (b * c - a * d) / (d - c); ` `    ``return` `X; ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``int` `a = 2, b = 3, c = 4, d = 5; ` `    ``Console.Write(getX(a, b, c, d)); ` `} ` `} ` ` `  `// The code is contributed by Tushil. `

Output:

```2
```

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Improved By : mohit kumar 29, jit_t