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:
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Number of ways to obtain each numbers in range [1, b+c] by adding any two numbers in range [a, b] and [b, c]
- Ratio of mth and nth terms of an A. P. with given ratio of sums
- Find the number which when added to the given ratio a : b, the ratio changes to c : d
- Create new linked list from two given linked list with greater element at each node
- Check if N can be obtained by repetitive addition or subtraction of two given numbers
- Find a number K having sum of numbers obtained by repeated removal of last digit of K is N
- Rearrange an Array such that Sum of same-indexed subsets differ from their Sum in the original Array
- Program to find the count of coins of each type from the given ratio
- Generate original array from difference between every two consecutive elements
- Total distinct pairs from two arrays such that second number can be obtained by inverting bits of first
- Check whether two numbers are in silver ratio
- Check whether two numbers are in golden ratio
- Count of carry operations on adding two Binary numbers
- Number of triplets such that each value is less than N and each pair sum is a multiple of K
- Find the original matrix when largest element in a row and a column are given
- Minimize steps to reach K from 0 by adding 1 or doubling at each step
- Count distinct elements after adding each element of First Array with Second Array
- Minimum sum obtained from groups of four elements from the given array
- Check if sum Y can be obtained from the Array by the given operations
- Probability of obtaining Prime Numbers as product of values obtained by throwing N dices
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.