Comparison of Ratios

Introduction

Comparison of ratios means comparing the relationship between two or more ratios. Finding out how many times one number is greater than the other is required if you are comparing two numbers. Or, to put it another way, we must represent one number as a fraction of the other.

Unitary methods are used to calculate single unit values from given multiples. This method is commonly used to demonstrate the notion of ratio and proportion.

In this tutorial, we will discuss the comparison of ratios.

Proportions: Comparing Ratios

Ratio

• The ratio is a divisional comparison of two numbers or quantities. The ratio is represented by the symbol ':'.

• The two quantities in a ratio must be in the same unit.

• Two ratios are equal if the fractions that correspond to them are the same and are interchangeable

Proportion

• When the ratio of the first and second quantities equals the ratio of the third and fourth values, four quantities are said to be in proportion. To compare the two ratios, use the symbols '::' or '='.

The sequence of terms in proportion matters. For instance, 3, 8, 24, and 64 are in proportion, but 3, 8, 64, and 24 are not.

Types of Proportions: Direct and Inverse

Direct Proportion:

• In mathematics, a direct proportion is a comparison of two integers where the ratio of the two numbers equals a fixed amount. According to the definition of proportion, two ratios are in proportion when they are equal. The proportions are represented by the symbol " $\mathrm{\varpropto}$.".

• The two quantities are said to be in a direct proportion when the relationship between them is such that if we increase one, the other will also increase, and if we decrease one, the other quantity will also decrease.

• For instance, if there are two quantities, x and y, where x is the number of candies and y is the total amount spent, if we buy more candies, we will have to pay more money, and if we buy fewer candies, we will be paying less money.

Inverse Proportion:

• Two quantities are said to be in inverse proportion when they are related to one another in this way, that is, when a rise in one quantity causes a reduction in the other and vice versa.

• The sum of the two provided quantities equals a constant amount in inverse proportion.

• If an increase in one causes a reduction in the other and a drop in one causes an increase in the other, two quantities are said to be in inverse proportion.

Solved Examples

1) A completes his work in 15 days, whereas "B" takes 10 days. How many days will the same work take if they collaborate?

Answer − Work of A in a day will be $\mathrm{=\:\frac{1}{15}}$

Similarly, work of B in a day will be $\mathrm{=\:\frac{1}{10}}$

Total work done by a and b together in a day $\mathrm{=\:\frac{1}{15}\:+\:\frac{1}{10}}$

$\mathrm{=\:\frac{5}{30}\:=\:\frac{1}{6}m}$

2) An automobile traveling at 150 k mph travels 450 kilometers. How long will it take to travel 300 kilometers?

Answer − $\mathrm{Speed\:=\:\frac{Distance}{Time}}$

$$\mathrm{time\:=\:\frac{450}{150}\:=\:3\:hours}$$

$$\mathrm{Time\:=\:3\:hours}$$

When using the unitary technique,

$$\mathrm{450\:km\:=\:3\:hours}$$

$$\mathrm{1\:km\:=\:\:\frac{3}{450}\:hour}$$

For 300 km, time taken $\mathrm{=\frac{3}{450}\times\:300\:=\:2\:hours}$

3) If Vivek buys 10 pens for 50$ then find the cost per pen?

Answer − It is given that Vivek buys 10 pens for 50 rupees, and we have to find the cost per pen.

Cost per pen= 50$/10 pen

By simplifying, we get

Cost per pen= 5$/ pen.

4) Find the unit rate if a man can type 60 words in 5 minutes?

Answer − It is given that the man can type 60 words in a 5 minute, then the unit rate will be given as 60 words /5 minute

By simplifying, we get 12 words per minute

5) If a student can solve 100 questions in 2 hours, then find the unit rate?

Answer − According to the question, a student can solve 100 questions in 2 hours; then by using the rate formula, we can say that the unit rate will be − 100 questions / 2 hour

By simplifying, we get 50 questions/hour

6) Calculate the unit rate if a fruit shop sells a dozen berries for $24?

Answer − We know that one dozen is equal to 12, and the price of 12 berries is $24 per unit cost of berries= 24$/12berries .

By simplifying, we get

per unit cost of berries = 2$/berries

7) If a man buys 10 mobiles for 100000$ then find the cost per mobile?

Answer − It is given that a man buys 10 mobiles for 100000$, then the cost per mobile will be given as

Cost per phone=100000$/10mobile

By simplifying, we get,

Cost per phone=100000=$/mobile.

8) Akash's monthly salary is $20,000, while Arjun's annual income is $360,000. Find the ratio of their savings if each of them has a monthly spend of $10,000.

Answer − Akash's monthly savings $\mathrm{=\:(20,000\:-\:10,000)\:=\:$100,000}$

Arjun's 12-month earnings = $360000

Arjun's monthly income $\mathrm{=\:\frac{360000}{12}\:=\:$30000}$

Arjun's monthly savings $\mathrm{=\:(30000\:-\:10000)\:=\:$20000}$

As a result, Akash and Arjun's savings ratio is $\mathrm{=\:10000\:\colon\:20000\:=\:1\:\colon\:2}$

9) The price of eight apples is $120. Determine the number of apples that may be bought with $240

Answer − Assume the cost of 8 apples is 120. As a result, the cost of one apple is $15.

Now, the number of apples available for purchase in 1 $\mathrm{$\:=\:\frac{1}{15}}$

As a result, the number of apples that may be purchased with $\mathrm{$240\:=\:\frac{1}{15}\times\:240\:=\:16}$

Conclusion

The term ratio refers to the quantitative relationship between two quantities or numbers. The concepts of ratio, proportion, and variation are critical in math and in everyday life. The ratio can be written in two ways: as a fraction or with a colon.

FAQs

1. What Does a Ratio Comparison Mean?

When two or more ratios are compared, their relationship is also compared. The ratio is the quantitative relationship between two quantities or numbers, and when three or more quantities are involved, a comparison of ratios is required.

2. What is the ratio?

The ratio is a divisional comparison of two numbers or quantities. The ratio is represented by the symbol ':'.

3. What is the proportion?

When the ratio of the first and second quantities equals the ratio of the third and fourth values, four quantities are said to be in proportion.

4. What do you mean by direct proportion?

The two quantities are said to be in a direct proportion when the relationship between them is such that if we increase one, the other will also increase, and if we decrease one, the other quantity will also decrease.

5. What do you mean by inverse proportion?

Two quantities are said to be in inverse proportion when they are related to one another in this way, that is, when a rise in one quantity causes a reduction in the other and vice versa.