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Comparison of Ratio

This is one of the most important calculations and is extensively used in DI. On an average, if somebody does 100 calculations in DI at least 8 to 10 calculations will be from comparing the ratios.
 
Normally, there are two methods to compare two or more than two ratios:

Cross multiplication method

Example

Let us compare 11/15 and 13/18.

 

 

Cross multiplying numerator of 1st fraction with the denominator of 2nd fraction and denominator of 1st fraction with the numerator of 2nd fraction,

 

11 × 18 13 × 15
198 195


Since, 198 is greater than 195 the 1st fraction (11/15) is greater than the 2nd fraction (13/18).

 

Decimal calculation

Description: 2373.png Description: 2382.png

Obviously, here the 1st fraction
Description: 2391.png is greater than the 2nd fraction Description: 2400.png.
 
However, if we have to compare 3156/5438 and 3423/5822, then using any of the above two methods becomes cumbersome and time-consuming.
 
Here, we will compare ratios with the help of percentage.

Percentage comparison

Let us first understand this with the help of the following ratios
 
1st Case Description: 2409.png
 
2nd Case Description: 2418.png
 
3rd Case Description: 2427.png

In the 1st case, percentage change in numerator (100%
) = percentage change in denominator (100%), so ratios are equal.
 
In the 2nd case, percentage change in the numerator (200%) > percentage change in the denominator (100%), so the 2nd ratio is greater than the 1st ratio.
 
In the 3rd case, percentage change in the numerator (200%) < percentage change in the denominator (300%), so the 1st ratio is greater than the 2nd ratio.
 
This particular example can also be seen as a general rule for determining the order of ratios.




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