Definition and difference between ratio and proportion for CLAT - Practice Questions & MCQ

Definition:

A ratio is a comparison between two quantities, showing the relative size of one quantity to another. It is often expressed in the form `a:b`, where "a" and "b" are the two quantities. 

Converting Ratio to Percentage:

Given a ratio `a:b`, the percentage representation of "a" in terms of the whole (a+b) is given by:

Converting Ratio to Decimal:

Given a ratio `a:b`, the decimal representation of "a" in terms of the whole (a+b) is:

Foundation Building Questions:

Question:

The number of male employees in a company is in the ratio 7:3 to the number of female employees. If the number of male employees is 105, find the percentage of female employees.

Solution:

Given ratio of male to female employees = 7:3

Number of male employees = 7x

Number of female employees = 3x

Given 7x = 105

=> x = 15

Number of female employees

Total employees

Percentage of female employees

Tips and Tricks:

1. Cross-Multiplication: This method is handy to quickly compare two ratios. If you have two ratios a:b and c:d, you can compare them by looking at the products ad and bc. If ad > bc, then the ratio a:b is greater.

2. Unitary Method: If you have the ratio and one of the actual values, always find the value of 1 unit first (as shown in the previous year question's solution). It simplifies calculations and can be applied uniformly to most problems.

3. Percentage and Decimal: Remember, ratios give a relationship between two parts. Percentages and decimals give the proportion of one part to the whole. Switching between these can provide insights into many questions.

4. Break Down Complex Ratios: If given a complex ratio such as 2:3:4, and you know the total or one part, break it down into simpler ratios (with respect to one part) to make calculations more straightforward.

When studying and practising, make sure to regularly solve problems from previous years. This helps in understanding the pattern and nature of questions, making the actual exam more approachable.