Complementary Ratios

Complementary ratios are ratios that when added together are equal to 1. In other words, if you have two ratios that are complementary, they will always add up to 1.

Example 1:

Let's say you have two ratios:

- Ratio A: 2:3
- Ratio B: x:y

To find a ratio that is complementary to Ratio A, we need to find a ratio that when added to 2:3, gives us a total of 1.

- 2:3 + x:y = 1

To solve for x and y, we can use cross-multiplication:

- 2y + 3x = 3y + 2x
- x = 3y - 2y
- x = y

So, Ratio B would be y:y or 1:1.

Example 2:

- Ratio C: 4:5
- Ratio D: a:b

To find a ratio that is complementary to Ratio C, we need to find a ratio that when added to 4:5, gives us a total of 1.

- 4:5 + a:b = 1

Again, we can use cross-multiplication to solve for a and b:

- 4b + 5a = 5b + 4a
- a = 5b - 4b
- a = b

So, Ratio D would be b:b or 1:1.

Summary

- Complementary ratios are ratios that add up to 1 when added together.
- To find a ratio that is complementary to another ratio, we need to solve for the missing values using cross-multiplication.
- In both examples, the complementary ratio was found to be 1:1.

We should keep in mind that Operating Profit Ratio and Operating Ratio are complementary to each other and thus if we deduct one of the two ratios from 100, another ratio will obtain. Objective: The objective of computing Operating Ratio is to assess the operational efficiency of the business.