Ratio and Proportion Tnpsc

Ratio and Proportion

Ratio and proportion are mathematical concepts that are closely related. A ratio is a comparison of two or more quantities, while a proportion is an equation that states two ratios are equal.

A ratio expresses the relationship between two or more numbers. It can be written in different forms, such as using the word “to” or a colon (:). For example, the ratio of girls to boys in a class could be 2:3 or 2 to 3.

Proportion, on the other hand, compares two ratios and states that they are equal. It can be expressed using the symbol “=”, such as in the equation 2:3 = 4:6. This means that the ratio of girls to boys is the same as the ratio of 4:6.

Ratios and proportions are used in various fields, such as cooking, finance, construction, and statistics. They help in making comparisons, solving problems, and making predictions.

To solve problems involving ratios and proportions, you can use cross-multiplication, where you multiply the numerator of one ratio with the denominator of the other ratio. This can help you find the unknown value or verify if two ratios are proportional.

Here are a few examples of ratios:

  1. Recipe Ratios: In a recipe, ingredients are often listed in ratios to ensure the right proportions. For example, a pancake recipe might call for a ratio of 2 cups of flour to 1 cup of milk.
  2. Financial Ratios: Financial ratios are used to analyze a company’s financial performance. For instance, the debt-to-equity ratio compares the company’s total debt to its shareholder’s equity.
  3. Speed Ratios: Speed ratios compare the speeds of different objects or vehicles. For instance, if a car travels 60 miles in 2 hours, its speed ratio would be 60 miles to 2 hours, or 30 miles per hour.
  4. Scale Ratios: Scale ratios are used in maps, models, and architectural blueprints to represent the relationship between the measurements in the model and the actual measurements of the object or area.
  5. Population Ratios: Population ratios compare various population groups. For example, the ratio of males to females in a town might be 3:2, meaning there are three males for every two females.

Ratio Problems

Example 1:
The ratio of boys to girls in a class is 3:5. If there are 48 students in total, how many boys are there?

To solve this problem, we can set up a proportion. Let x represent the number of boys.

  • Boys: Girls = 3:5
  • Boys + Girls = Total students

Writing this as a proportion, we get: 3/5 = x/(48-x)

To solve for x, we can cross-multiply: 3(48-x) = 5x
Simplifying the equation, we get: 144 - 3x = 5x
Rearranging the equation, we have: 8x = 144
Dividing both sides by 8, we find: x = 18

Therefore, there are 18 boys in the class.

Example 2:
A recipe calls for a ratio of 2 cups of flour to 1 cup of milk. If you want to make 6 cups of flour, how much milk do you need?

To solve this problem, we can set up a proportion. Let x represent the amount of milk needed.

  • Flour: Milk = 2:1

Writing this as a proportion, we get: 2/1 = 6/x

To solve for x, we can cross-multiply: 2x = 6
Dividing both sides by 2, we find: x = 3

Therefore, you would need 3 cups of milk.

Proportional Problems

Sure! Here are a few examples of proportional problems:

Example 1:
A car can travel 200 miles on 8 gallons of gas. How far can it travel on 4 gallons of gas?

To solve this problem, we can set up a proportion. Let x represent the distance the car can travel on 4 gallons of gas.

  • Distance: Gas = 200:8

Writing this as a proportion, we get: 200/8 = x/4

To solve for x, we can cross-multiply: 8x = 800
Dividing both sides by 8, we find: x = 100

Therefore, the car can travel 100 miles on 4 gallons of gas.

Example 2:
A scale model of a building has a height of 12 inches. If the actual building has a height of 60 feet, what is the scale ratio of the model to the actual building?

To solve this problem, we can set up a proportion. Let x represent the scale ratio of the model to the actual building.

  • Model Height: Actual Height = 12:60

Writing this as a proportion, we get: 12/60 = x/1

To solve for x, we can cross-multiply: 60x = 12
Dividing both sides by 60, we find: x = 0.2

Therefore, the scale ratio of the model to the actual building is 1:0.2.

* * All the Notes in this blog, are referred from Tamil Nadu State Board Books and Samacheer Kalvi Books. Kindly check with the original Tamil Nadu state board books and Ncert Books.
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