Ratio Chapter Notes | Quantitative Aptitude for CA Foundation PDF Download

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Ratio Chapter Notes | Quantitative Aptitude for CA Foundation

Ratio

  •  A ratio represents the comparison of the sizes of two or more quantities of the same type through division. 
  •  If a and b are two quantities of the same type (in identical units), the fraction a/b denotes the ratio of a to b. 
  •  This is expressed as a : b
  •  Therefore, the ratio of a to b is equivalent to a/b or a : b
  •  The quantities a and b are referred to as the terms of the ratio, with a being the first term or antecedent, and b being the second term or consequent

Ratio Chapter Notes | Quantitative Aptitude for CA Foundation

For instance, in the ratio 5 : 6, 5 and 6 are identified as the terms of the ratio, where 5 is the first term and 6 is the second term.

Remarks 

  • Both components of a ratio can be multiplied or divided by the same (non-zero) number.
  • A ratio is typically presented in its simplest form.

Question for Chapter Notes: Ratio
Try yourself:
If the ratio of apples to oranges in a basket is 3:2, and there are 15 oranges, how many apples are there in the basket?
View Solution

Illustration I: 12 : 16 = 12/16 = (3 × 4)/(4 × 4) = 3/4 = 3 : 4 

  • The order of the terms in a ratio is important. 

Illustration II: 

3 : 4 is not same as 4 : 3. 

  • Ratio exists only between quantities of the same kind. 

Illustration III: 
(i) There is no ratio between number of students in a class and the salary of a teacher.
(ii) There is no ratio between the weight of one child and the age of another child.

  • Quantities to be compared (by division) must be in the same units. 

Illustration IV: 
(i) Ratio between 150 gm and 2 kg
= Ratio between 150 gm and 2000 gm
= 150/2000 = 3/40 = 3 : 40 

(ii) Ratio between 25 minutes and 45 seconds
= Ratio between (25 × 60) sec. and 45 sec.
= 1500/45 = 100/3 = 100 : 3 

Illustration V: 
(i) Ratio between 3 kg & 5 kg = 3/5
To compare two ratios, convert them into equivalent like fractions. 

Illustration VI: To find which ratio is greater _____________
Ratio Chapter Notes | Quantitative Aptitude for CA Foundation
Sol:
Ratio Chapter Notes | Quantitative Aptitude for CA Foundation

3.6 : 4.8 = 3.6/4.8 = 36/48 = 3/4
L.C.M of 10 and 4 is 20.
So, 7/10 = (7 × 2)/(10 × 2) = 14/20
And 3/4 = (3 × 5)/(4 × 5) = 15/20
As 15 > 14 so, 15/20 > 14/20 i. e. 3/4 > 7/10
Hence, 3.6 : 4.8 is a greater ratio. 

  • If a quantity increases or decreases in the ratio a : b then the new quantity = b/a of the original quantity/a

The fraction by which the original quantity is multiplied to get a new quantity is called the factor multiplying ratio. 

Illustration VII: Rounaq weighs 56.7 kg. If he reduces his weight in the ratio 7 : 6, find his new weight.
Sol: Original weight of Rounaq = 56.7 kg
He reduces his weight in the ratio 7 : 6
His new weight Ratio Chapter Notes | Quantitative Aptitude for CA Foundation

Applications: 
Example 1: Simplify the ratio 1/3 : 1/8 : 1/6 
Sol: 
L.C.M. of 3, 8 and 6 is 24. 1/3 : 1/8 : 1/6 = 1 × 24/3 : 1 × 24/8 : 1 × 24/6 = 8 : 3 : 4 

Example 2: The ratio of the number of boys to the number of girls in a school of 720 students is 3 : 5. If 18 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of the number of boys to the number of girls may change to 2 : 3. 
Sol: 
The ratio of the number of boys to the number of girls = 3 : 5
Sum of the ratios = 3 + 5 = 8
So, the number of boys in the school = (3 × 720)/8 = 270
And the number of girls in the school = (5 × 720)/8 = 450
Let the number of new boys admitted be x, then the number of boys becomes (270 + x).
After admitting 18 new girls, the number of girls becomes 450 + 18 = 468
According to given description of the problem, (270 + x)/468 = 2/3
or, 3 (270 + x) = 2 x 468
or, 810 + 3x = 936 or, 3x = 126 or, x = 42.
Hence the number of new boys admitted = 42.

Inverse Ratio 

One ratio is the inverse of another if their product equals 1. Therefore, a : b is the inverse of b : a and vice versa.

Some Properties of Ratios: 

  1. A ratio a : b is said to be of greater inequality if a>b and of lesser inequality if a<b. 
  2. The ratio compounded of the two ratios a : b and c : d is ac : bd. For example compound ratio of 3 : 4 and 5 : 7 is 15 : 28. The Compound ratio of 2 : 3, 5 : 7 and 4 : 9 is 40 : 189. 
  3. A ratio compounded of itself is called its duplicate ratio. Thus a2 : b2 is the duplicate ratio of a : b. Similarly, the triplicate ratio of a : b is a3 : b3. For example, the duplicate ratio of 2 : 3 is 4 : 9. Triplicate ratio of 2 : 3 is 8 : 27. 
  4. The sub-duplicate ratio of a : b is √a : √b and the sub-triplicate ratio of a : b is ∛a : ∛b .
    For example, the sub-duplicate ratio of 4 : 9 is √4 : √9 = 2 : 3
    And sub-triplicate ratio of 8 : 27 is ∛8 : ∛27 = 2 : 3. 
  5. If the ratio of two similar quantities can be expressed as rational numbers, the quantities are said to be commensurable; otherwise, they are said to be incommensurable. 3 : 2 cannot be expressed as the ratio of two integers and therefore, √3 and √2 are incommensurable quantities. 
  6. Continued Ratio is the relation (or comparison) between the magnitudes of three or more quantities of the same kind. The continued ratio of three similar quantities a, b, c is written as a : b : c.

Applications: 
Illustration I: The continued ratio of ₹ 200, ₹ 400 and ₹ 600 is ₹ 200 : ₹ 400 : ₹ 600 = 1 : 2 : 3.
Example 1: The monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenditures are in the ratio 7 : 9. If each saves ₹ 50 per month, find their monthly incomes. 
Sol: 
Let the monthly incomes of two persons be ₹ 4x and ₹ 5x so that the ratio is ₹ 4x : ₹ 5x = 4 : 5. If each saves ₹ 50 per month, then the expenditures of two persons are ₹ (4x – 50) and ₹ (5x – 50).
Ratio Chapter Notes | Quantitative Aptitude for CA Foundation
or, 36x – 35x = 450 – 350, or, x = 100
Hence, the monthly incomes of the two persons are ₹ 4 × 100 and ₹ 5 × 100 i.e. ₹ 400 and ₹ 500.

Example 2: The ratio of the prices of two houses was 16 : 23. Two years later when the price of the first has increased by 10% and that of the second by ₹ 477, the ratio of the prices becomes 11 : 20. Find the original prices of the two houses. 
Sol:
Let the original prices of two houses be ₹ 16x and ₹ 23x respectively. Then by the given conditions,
Ratio Chapter Notes | Quantitative Aptitude for CA Foundation
Ratio Chapter Notes | Quantitative Aptitude for CA Foundation
or, 352x – 253x = 5247, or, 99x = 5247;  x = 53 Hence, the original prices of two houses are ₹ 16 × 53 and ₹ 23 × 53 i.e. ₹ 848 and ₹ 1,219. 

Example 3: Find in what ratio will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15 : 11 and an increment in their wages in the ratio 22 : 25. 
Sol: 
Let x be the original number of workers and ₹ y the (average) wages per workers. Then the total wages before changes = ₹ xy. After reduction, the number of workers = (11x)/15 After increment, the (average) wages per workers = ₹ (25y)/22
∴ The total wages after changes Ratio Chapter Notes | Quantitative Aptitude for CA Foundation
Thus, the total wages of workers get decreased from ₹ xy to ₹ 5xy/6
Hence, the required ratio in which the total wages decrease is Ratio Chapter Notes | Quantitative Aptitude for CA Foundation

The document Ratio Chapter Notes | Quantitative Aptitude for CA Foundation is a part of the CA Foundation Course Quantitative Aptitude for CA Foundation.
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FAQs on Ratio Chapter Notes - Quantitative Aptitude for CA Foundation

1. What are the different types of ratios used in CA Foundation exams?
Ans. The main types of ratios used in CA Foundation exams include liquidity ratios, profitability ratios, solvency ratios, and efficiency ratios. Each type serves a different purpose in analyzing a company's financial health.
2. How do liquidity ratios help in financial analysis?
Ans. Liquidity ratios, such as the current ratio and quick ratio, measure a company's ability to meet its short-term obligations. They help stakeholders understand the company's financial stability and short-term solvency.
3. What is the significance of profitability ratios in evaluating a business?
Ans. Profitability ratios, like the net profit margin and return on equity, indicate how efficiently a company generates profit relative to its revenue or assets. They are crucial for assessing a company's financial performance and operational efficiency.
4. Can you explain the concept of solvency ratios?
Ans. Solvency ratios, including the debt-to-equity ratio and interest coverage ratio, assess a company's long-term financial stability and ability to meet long-term obligations. They are essential for understanding a company's capital structure and financial risk.
5. How can efficiency ratios impact investment decisions?
Ans. Efficiency ratios, such as inventory turnover and asset turnover, evaluate how effectively a company utilizes its assets to generate revenue. Investors use these ratios to gauge operational performance and make informed investment decisions.
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