Sum of two numbers if the original ratio and new ratio obtained by adding a given number to each number is given
Given a ratio a : b of two unknown numbers. When both the numbers are incremented by a given integer x, the ratio becomes c : d. The task is to find the sum of the two numbers.
Input: a = 2, b = 3, c = 8, d = 9, x = 6
Original numbers are 2 and 3
Original ratio = 2:3
After adding 6, ratio becomes 8:9
2 + 3 = 5
Input: a = 1, b = 2, c = 9, d = 13, x = 5
Approach: Let the sum of the numbers be S. Then, the numbers can be (a * S)/(a + b) and (b * S)/(a + b).
Now, as given:
(((a * S) / (a + b)) + x) / (((b * S) / (a + b)) + x) = c / d or ((a * S) + x * (a + b)) / ((b * S) + x * (a + b)) = c / d So, S = (x * (a + b) * (c - d)) / (ad - bc)
Below is the implementation of the above approach:
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