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++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to return the// required number Xint getX(int a, int b, int c, int d){ int X = (b * c - a * d) / (d - c); return X;}// Driver codeint main(){ int a = 2, b = 3, c = 4, d = 5; cout << getX(a, b, c, d); return 0;} |
Java
// Java implementation of the approachimport java.io.*;class GFG { // Function to return the// required number Xstatic int getX(int a, int b, int c, int d){ int X = (b * c - a * d) / (d - c); return X;}// Driver codepublic 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 Xdef getX(a, b, c, d): X = (b * c - a * d) // (d - c) return X# Driver codea = 2b = 3c = 4d = 5print(getX(a, b, c, d))# This code is contributed by mohit kumar 29 |
C#
// C# implementation of the approachusing System;class GFG{ // Function to return the// required number Xstatic int getX(int a, int b, int c, int d){ int X = (b * c - a * d) / (d - c); return X;}// Driver codestatic 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. |
Javascript
<script>// javascript implementation of the approach // Function to return the// required number Xfunction getX(a , b , c , d){ var X = (b * c - a * d) / (d - c); return X;}// Driver codevar a = 2, b = 3, c = 4, d = 5;document.write(getX(a, b, c, d));// This code is contributed by 29AjayKumar </script> |
Output:
2
Time Complexity: O(1), since there is a basic arithmetic operation that takes constant time.
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 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!