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

Edited By admin | Updated on Oct 06, 2023 06:35 PM | #CLAT

Quick Facts

2 Questions around this concept.

Solve by difficulty

In three similar vessels, the ratio of water and milk is 6:7, 5:9, and 8:7, respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?

2431:3781

3691:4499

4381:5469

None of these

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Three containers of capacity 20L, 5L, and 9L contain a mixture of milk and water with milk concentrations of 90%, 80%, and 70%, respectively. The contents of three containers are emptied into a large vessel. What is the approximate ratio of milk to water in the resultant mixture?

3:1

4:1

5:1

2:1

View Solution

Concepts Covered - 1

Definition and difference between ratio and proportion

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:

$\mathrm{\text { Percentage of } a=\frac{a}{a+b} \times 100 \%}$

Converting Ratio to Decimal:

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

$\mathrm{\text { Decimal of } a=\frac{a}{a+b} }$

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 $= 3x = 3 \times 15 = 45$

Total employees $= 105 + 45 = 150$

Percentage of female employees $= (45/150) \times 100% = 30%$

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.