Given a:b and b:c. The task is to write a program to find ratio a:b:c**Examples:**

Input:a:b = 2:3, b:c = 3:4Output:2:3:4Input:a:b = 3:4, b:c = 8:9Output:6:8:9

**Approach:** The trick is to make the common term ‘b’ equal in both ratios. Therefore, multiply the first ratio by b_{2} (b term of second ratio) and the second ratio by b_{1}.

Given:a:b_{1}and b_{2}:cSolution:a:b:c = (a*b_{2}):(b_{1}*b_{2}):(c*b_{1})For example:

If a : b = 5 : 9 and b : c = 7 : 4, then find a : b : c.Solution:

Here, Make the common term ‘b’ equal in both ratios.

Therefore, multiply the first ratio by 7 and the second ratio by 9.

So, a : b = 35 : 63 and b : c = 63 : 36

Thus, a : b : c = 35 : 63 : 36

Below is the implementation of the above approach:

## C++

`// C++ implementation of above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to print a:b:c` `void` `solveProportion(` `int` `a, ` `int` `b1, ` `int` `b2, ` `int` `c)` `{` ` ` `int` `A = a * b2;` ` ` `int` `B = b1 * b2;` ` ` `int` `C = b1 * c;` ` ` `// To print the given proportion` ` ` `// in simplest form.` ` ` `int` `gcd = __gcd(__gcd(A, B), C);` ` ` `cout << A / gcd << ` `":"` ` ` `<< B / gcd << ` `":"` ` ` `<< C / gcd;` `}` `// Driver code` `int` `main()` `{` ` ` `// Get the ratios` ` ` `int` `a, b1, b2, c;` ` ` `// Get ratio a:b1` ` ` `a = 3;` ` ` `b1 = 4;` ` ` `// Get ratio b2:c` ` ` `b2 = 8;` ` ` `c = 9;` ` ` `// Find the ratio a:b:c` ` ` `solveProportion(a, b1, b2, c);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of above approach` `import` `java.util.*;` `import` `java.lang.*;` `import` `java.io.*;` `class` `GFG{` `static` `int` `__gcd(` `int` `a,` `int` `b){` ` ` `return` `b==` `0` `? a : __gcd(b, a%b);` `} ` `// Function to print a:b:c` `static` `void` `solveProportion(` `int` `a, ` `int` `b1, ` `int` `b2, ` `int` `c)` `{` ` ` `int` `A = a * b2;` ` ` `int` `B = b1 * b2;` ` ` `int` `C = b1 * c;` ` ` ` ` `// To print the given proportion` ` ` `// in simplest form.` ` ` `int` `gcd = __gcd(__gcd(A, B), C);` ` ` ` ` `System.out.print( A / gcd + ` `":"` ` ` `+ B / gcd + ` `":"` ` ` `+ C / gcd);` `}` ` ` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` ` ` `// Get the ratios` ` ` `int` `a, b1, b2, c;` ` ` ` ` `// Get ratio a:b1` ` ` `a = ` `3` `;` ` ` `b1 = ` `4` `;` ` ` ` ` `// Get ratio b2:c` ` ` `b2 = ` `8` `;` ` ` `c = ` `9` `;` ` ` ` ` `// Find the ratio a:b:c` ` ` `solveProportion(a, b1, b2, c);` `}` `}` |

## Python 3

`# Python 3 implementation` `# of above approach` `import` `math` `# Function to print a:b:c` `def` `solveProportion(a, b1, b2, c):` ` ` `A ` `=` `a ` `*` `b2` ` ` `B ` `=` `b1 ` `*` `b2` ` ` `C ` `=` `b1 ` `*` `c` ` ` `# To print the given proportion` ` ` `# in simplest form.` ` ` `gcd1 ` `=` `math.gcd(math.gcd(A, B), C)` ` ` `print` `( ` `str` `(A ` `/` `/` `gcd1) ` `+` `":"` `+` ` ` `str` `(B ` `/` `/` `gcd1) ` `+` `":"` `+` ` ` `str` `(C ` `/` `/` `gcd1))` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `# Get ratio a:b1` ` ` `a ` `=` `3` ` ` `b1 ` `=` `4` ` ` `# Get ratio b2:c` ` ` `b2 ` `=` `8` ` ` `c ` `=` `9` ` ` `# Find the ratio a:b:c` ` ` `solveProportion(a, b1, b2, c)` `# This code is contributed` `# by ChitraNayal` |

## C#

`// C# implementation of above approach` `using` `System;` `class` `GFG` `{` `static` `int` `__gcd(` `int` `a,` `int` `b)` `{` ` ` `return` `b == 0 ? a : __gcd(b, a % b);` `}` `// Function to print a:b:c` `static` `void` `solveProportion(` `int` `a, ` `int` `b1,` ` ` `int` `b2, ` `int` `c)` `{` ` ` `int` `A = a * b2;` ` ` `int` `B = b1 * b2;` ` ` `int` `C = b1 * c;` ` ` `// To print the given proportion` ` ` `// in simplest form.` ` ` `int` `gcd = __gcd(__gcd(A, B), C);` ` ` `Console.Write( A / gcd + ` `":"` `+` ` ` `B / gcd + ` `":"` `+` ` ` `C / gcd);` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `// Get the ratios` ` ` `int` `a, b1, b2, c;` ` ` `// Get ratio a:b1` ` ` `a = 3;` ` ` `b1 = 4;` ` ` `// Get ratio b2:c` ` ` `b2 = 8;` ` ` `c = 9;` ` ` `// Find the ratio a:b:c` ` ` `solveProportion(a, b1, b2, c);` `}` `}` `// This code is contributed` `// by Akanksha Rai(Abby_akku)` |

## PHP

`<?php` `// PHP implementation of above approach` `function` `__gcd(` `$a` `, ` `$b` `)` `{` ` ` `return` `$b` `== 0 ? ` `$a` `: __gcd(` `$b` `, ` `$a` `% ` `$b` `);` `}` `// Function to print a:b:c` `function` `solveProportion(` `$a` `, ` `$b1` `, ` `$b2` `, ` `$c` `)` `{` ` ` `$A` `= ` `$a` `* ` `$b2` `;` ` ` `$B` `= ` `$b1` `* ` `$b2` `;` ` ` `$C` `= ` `$b1` `* ` `$c` `;` ` ` `// To print the given proportion` ` ` `// in simplest form.` ` ` `$gcd` `= __gcd(__gcd(` `$A` `, ` `$B` `), ` `$C` `);` ` ` `echo` `(` `$A` `/ ` `$gcd` `) . ` `":"` `.` ` ` `(` `$B` `/ ` `$gcd` `) . ` `":"` `. (` `$C` `/ ` `$gcd` `);` `}` `// Driver code` `// Get the ratios` `// Get ratio a:b1` `$a` `= 3;` `$b1` `= 4;` `// Get ratio b2:c` `$b2` `= 8;` `$c` `= 9;` `// Find the ratio a:b:c` `solveProportion(` `$a` `, ` `$b1` `, ` `$b2` `, ` `$c` `);` `// This code is contributed by mits` `?>` |

## Javascript

`<script>` ` ` `// Javascript implementation of above approach` ` ` ` ` `function` `__gcd(a, b)` ` ` `{` ` ` `return` `b == 0 ? a : __gcd(b, a % b);` ` ` `}` ` ` `// Function to print a:b:c` ` ` `function` `solveProportion(a, b1, b2, c)` ` ` `{` ` ` `let A = a * b2;` ` ` `let B = b1 * b2;` ` ` `let C = b1 * c;` ` ` `// To print the given proportion` ` ` `// in simplest form.` ` ` `let gcd = __gcd(__gcd(A, B), C);` ` ` `document.write( A / gcd + ` `":"` `+ B / gcd + ` `":"` `+ C / gcd);` ` ` `}` ` ` `// Get the ratios` ` ` `let a, b1, b2, c;` ` ` ` ` `// Get ratio a:b1` ` ` `a = 3;` ` ` `b1 = 4;` ` ` ` ` `// Get ratio b2:c` ` ` `b2 = 8;` ` ` `c = 9;` ` ` ` ` `// Find the ratio a:b:c` ` ` `solveProportion(a, b1, b2, c);` ` ` ` ` `// This code is contributed by divyeshrabadiya07.` `</script>` |

**Output:**

6:8:9

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