Mastering Ratio and Proportion Questions: Tips, Tricks, and Techniques!

Stuck figuring out how many cookies your friend deserves if you bake a batch? Ratios and proportions are the secret weapons to solve these problems (and many more)! This guide will turn you into a master of ratio and proportion questions. We'll break down what ratios and proportions are in a way that's easy to understand. With fun examples and clear steps, you'll be a whiz at comparing things and solving tricky fraction problems quickly!

Ratio and proportion are two key mathematical concepts that are used to compare two or more quantities. A ratio is a numerical comparison of two numbers, but a proportion is an equation stating that two ratios are equal.

This tutorial will teach us how to compute ratios and proportions using various problems.

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Let us begin with a formal definition of Ratio and Proportion.

Table of Content

• What is Ratio?
• What is Proportion?
• Example of Ratio and Proportion
• Ratio and Proportion Questions
• Ratio and Proportion MCQ

What is Ratio?

The Ratio is a way to compare two quantities by division. In simple terms, it is a way to compare how much of one thing is compared to another thing.

It can be expressed in several ways, using a colon (e.g. 3:4) and using a division (e.g. 3/4). Sometimes the Ratio of two numbers can also be expressed using the word “to”.

Example: You have 7 red balls and 3 blue balls. Then the Ratio of:

• Red balls to Blue balls is 7:3.
• Blue balls to Red Balls is 3:7

Note: Two numbers must have the same unit of measurement.

What is Proportion?

A Proportion is an equation that states that two ratios are equal. In simple terms, it means that two ratios represent the same relationship between numbers.

It can be written as a fraction set equal to another fraction, such as a/b = c/d.

Example: For a recipe that calls for 2 cups of flour to make 12 cookies. If you want to make 6 cookies, you would use 1 cup of flour.

Here, the proportion will be:

2 cup of floor / 12 cookies = 1 cup of floor / 6 cookies

Until now, you have a clear understanding of what ratio and proportion are.

Now, let’s take one more example of Ratio and proportion together to understand better what Ratios and Proportions are and how to calculate them.

Example of Ratio and Proportion

You are making lemonade using a recipe that involves that require following ingredients:

Lemon = 4

Cup of Sugar = 1

Liters of Water = 2

Then the Ratio of lemon to sugar to water is 4:1:2, i.e., for every 4 lemons, you are using 1 cup of sugar and 2 litres of water.

Now, you decided to make lemonade of 12 lemons, so how much water and sugar do you need?

Here, the concept of proportion comes into action. Here, we will set up a proportion based on the original recipe.

For Lemons

• Original Ratio = 4 lemon
• New Quantity = 12 lemons

For Sugar

• Original Ratio = 1 cup of sugar
• New Quantity = x cup of sugar

For Water

• Original Ratio = 2 litres of water
• New Quantity = y litre of water

Now, using the proportion of lemon to calculate the proportion of water and sugar:

(4 lemons/1 cup of sugar) = (12 lemons/x cups of sugar)

Now, cross-multiplying, we get:

4*x = 12*1

=> x = 3

So, you will 3 cups of sugar for 12 lemons.

Similarly, you can calculate the proportion of water for 12 lemons.

(4 lemons/2 litres of water) = 12 lemons/y litres of water)

Cross-multiplying, we get:

4*y = 12*2

=> y = 6

So, you will need 6 litre of water to make lemonade of 12 lemons.

Hence, to make lemonade of 12 lemons, you have to add 3 cups of sugar and 6 litres of water to maintain the same taste as the original.

Ratio and Proportion Questions

1. Divide 50 into two people in a ratio of 3:2.

Answer: Let’s think of a question like you have to divide 50 into 5 equal parts to two people: the first person will take 3 parts of 50, and the second person will take the remaining 2 parts of 50.

therefore, 

First Person = (3/5) * 50 = 30

Second Person = (2/5) * 50 = 20

2. Are 2:3 and 4:6 equivalent ratios?

Answer: Yes, because 2/3 = 4/6 (simplifying the numerator and denominator, 4/6 = 2*2 / 2*3 = 2/3).

3. If 5 books cost INR 100, how much do 8 book cost?

Answer: As given

Cost of 5 books = 100

=> Cost of 1 book = 100/5 = 20

So, the cost of 8 books = 8*20 = 160

or

Let the cost of 8 books will be INR x

then, 

100/ 5 = x/8 (Cost of n book/ n number of books)

cross-multiplying both side, we get

100*8 = 5*x

=> x = 100*8/5 = 160

=> x = 160

Hence, the cost of 8 books will be INR 160.

4. The ratio of ages of A and B is 4:5. If the age of A is 24, then calculate the age of B.

Answer: Here, we will use the same concept we used in the above question.

Let the age of B is x, then

4/5 = 24/x

=> x = (24*5)/4 = 30

Hence, the age of B is 30 years.

5. In what ratio should water be mixed with juice to get a mixture containing 75% juice?

Answer: Let the ratio of water that should be mixed with the juice to get the mixture containing juice is x:1.

Therefore,

(x/x+1)*100 = 75

=> x/x+1 = 3/4 

=> x = 3

hence, the ratio is 3:1.

Till now, you have a clear understanding of how to calculate the ratio and proportion. So, let’s have some ratio and proportion questions for practice.

Ratio and Proportion MCQ

1. Two numbers are in the ratio 3:5. If their LCM is 75, what are the numbers?

A) 15, 25
B) 9, 15
C) 12, 20
D) 3, 5
Answer: A) 15, 25

2. The salaries of A, B, and C are in the ratio 2:3:5. If the increments of 15%, 10%, and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

A) 23:33:60
B) 3:3:6
C) 23:30:60
D) 10:10:20
Answer: A) 23:33:60

3. The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the students does not hold any scholarship?

A) 78%
B) 80%
C) 82%
D) 85%
Answer: A) 78%

4. In a bag, there are coins of 25 p, 10 p, and 5 p in the ratio of 1:2:3. If there is Rs. 30 in all, how many 5 p coins are there?

A) 50
B) 100
C) 150
D) 200
Answer: B) 100

5. A and B can complete a task in 10 and 15 days respectively. In how many days will they complete the task if they work together?
A) 5 days
B) 6 days
C) 7.5 days
D) 9 days

6. The population of a town increases annually in the ratio 11:10. If the population in the year 2020 was 110,000, what was the population in 2019?
A) 100,000
B) 105,000
C) 95,000
D) 90,000

7. Two trains travel at speeds in the ratio 4:5. If the first train takes 6 hours to cover a distance, how long will the second train take to cover the same distance?
A) 4.8 hours
B) 5.4 hours
C) 7.2 hours
D) 8 hours

8. If a dataset has values ranging from 0 to 1000 and needs to be scaled down to a range of 0 to 1, what will be the scaled value of 500?

A) 0.2
B) 0.5
C) 0.05
D) 5

9. In a binary classification task, if the ratio of true positives to false positives is 4:1 and there are 80 true positives, how many false positives are there?
A) 20
B) 25
C) 16
D) 10

10. If the learning rates tested on a model are in the ratio 1:10:100 and the smallest learning rate is 0.001, what is the largest learning rate tested?
A) 0.01
B) 0.1
C) 1
D) 10

Conclusion

A ratio is a numerical comparison of two numbers, but a proportion is an equation stating that two ratios are equal.

In this article, we have discussed how to solve the ratio and proportion questions. The article also consists of solved and unsolved questions for learning and practice.

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