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

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++

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// C++ implementation of the approach
#include <bits/stdc++.h>
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;
}

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Java

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// 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 

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Python

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# 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

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C#

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// 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.

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Output:

2


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Improved By : mohit kumar 29, jit_t