Tips and Tricks: Percentages | Quantitative Aptitude for SSC CGL PDF Download

Introduction 

Percentages are a basic math concept that show how much something is out of 100. They are used in many areas like finance, statistics, and daily life. Knowing how to work with percentages helps people compare amounts, calculate discounts, find profits, and analyze information better.

In the SSC CGL (Staff Selection Commission Combined Graduate Level) exam, percentages are very important. This exam tests candidates' math skills, and being good at percentages is key for solving problems about profit and loss, simple and compound interest, and understanding data. Being skilled in calculating percentages can help you answer questions quickly and correctly, which is crucial given the exam's time limits.

Basic Concepts of Percentages

• Percent: A way to measure something as a part of a total, where 1% means one part out of 100. For example, 1% is the same as 1 out of 100.
• Whole: The full amount or total that the percentage is talking about. For instance, the total number of students in a class.
• Part: The specific portion of the whole that the percentage refers to. For example, the number of students who got A grades in the class.

Percentages

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

(Part/Whole)x100

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Percentage Table with Common Fractions and their Percentage Equivalents

Convert Percentages to Decimals or Fractions:

Sometimes it’s easier to work with decimals or fractions rather than percentages. To convert a percentage to a decimal, divide by 100. To convert a percentage to a fraction, simply write it over 100 and simplify if possible.

Practice Decimal Equivalents of Common Fractions:

Knowing common decimal equivalents of fractions (e.g., 1/4 = 0.25, 1/2 = 0.5, 3/4 = 0.75) can speed up your calculations.

Solving Percentage Increase/Decrease:

To find the percentage increase or decrease between two values, use the formula:

• Percentage Change = [(New Value – Old Value) / |Old Value|] * 100

Calculate Reverse Percentages:

If you have the final amount and the percentage increase/decrease and need to find the original amount, you can use this formula:

• Original Value = Final Value / (1 ± Percentage/100)

​Percentages Tips and Tricks

Download the notes Tips and Tricks: Percentages

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Type 1: Problems based on Mixtures and Alligations

Understanding percentages is crucial for solving various mathematical problems, especially those involving mixtures and alligations. Mixtures refer to the combination of two or more substances, while alligation is a method used to find the average price or percentage of a mixture. Let's understand this with an example.

Example : A small container has 60l of milk and water mixture. It was made by mixing milk and water in which 80% is milk. Rohan came and added some water in the mixture. Now, find out how much water was added to the mixture that the percentage of milk became 60%?
Options:
A. 20 litre
B. 25 litre
C. 2 litre
D. 10 litre
Solution: Given, percentage of milk = 80%
It means, the percentage of water = 20%
In 60L of mixture, water = Let the water added = x Now,  (it is because in the new mixture milk is 60%, 100 – 60 = 40% water)1200 + 100x = 2400 + 40x100x – 40x = 2400 – 1200
60x = 1200
x= 20 litre
Correct option: A

Type 2: Problems based on Ratios and Fractions

Ratios and fractions are fundamental concepts in mathematics that describe relationships between quantities. A ratio is a comparison of two or more quantities that shows the relative size of one quantity to another, expressed in simplest form. A fraction, on the other hand, represents a part of a whole, consisting of a numerator and a denominator. 

Example:  If the numerator of a fraction is increased by 50% and the denominator is decreased by 10%, the value of the new fraction becomes 4/5 . Find the original fraction?
Options:
A. 12/21
B. 13/20
C. 12/25
D. 25/12
Solution: Let original numerator be x
Let original denominator be y
Let original fraction be x/y
According to the question,
Numerator of a fraction is increased by 50% = 150/100
Denominator is decreased by 10% = 90/100
Now, Correct option: C

Type 3: Problems based on Income, Salary, Expenditure

Understanding the concepts of income, salary, and expenditure is essential for effective financial management. Income refers to the money received, typically on a regular basis, for work or through investments. Salary is a fixed payment received by an employee, usually on a monthly or biweekly basis, in exchange for their services. Expenditure, on the other hand, encompasses all spending, including fixed and variable costs, that individuals or organizations incur. Analyzing these components helps individuals and businesses make informed decisions regarding budgeting, saving, and investing.

Example: Ajay spends 40% of his salary and saves Rs. 480 per month. Find his monthly salary.
Options:
A. 1000
B. 800
C. 600
D. 850
Solution: Let the salary of Ajay be x
He spends 40% which means he saves 60% of the salary.
60% of x = 480
x = 800 Therefore, his monthly salary = 800
Correct option: B

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Type 4:  Problems based on Population

Population problems are a fundamental aspect of mathematical studies, particularly in the fields of statistics and demographic analysis. These problems often involve the analysis of population growth, decline, and distribution, using mathematical models to predict future trends based on current and historical data.

Example: Delhi has the population of 3000. In the first year, the population decreases by 4%, and in the second year, it increases by 5%. Find the population at the end of two years?
Options:
A. 3024
B. Remains same
C. 3120
D. 2880
Solution: In the first year, the population decreases by 4% = 3000 x 96/100 = 2880
In the second year it increases by 5% = 2880 x 105 x 100 = 3024
Correct option: A

Type 5: Problems based on Profit and Loss

Profit and loss are fundamental concepts in the field of mathematics, particularly in business and finance.  Profit refers to the financial gain obtained when the revenue from sales exceeds the costs of producing or purchasing the goods sold. Conversely, loss occurs when the costs surpass the revenue generated. By analyzing profit and loss, individuals and businesses can gauge their financial performance and strategize accordingly.

Example: The cost price of 20 chairs is the same as the selling price of x tables. If the profit is 25%, then find the value of x?
Options:
A. 15
B. 20
C. 16
D. 18
Solution: Let the CP of each chair = 1
Therefore CP of x table = x
20 CP = X SP
Profit % = SP/CP
1.25=20/X
X=16
Correct option: C

Type 6: Percentage Tips and Tricks and Shortcuts

Example: If 20% of a = b, then b% of 20 is the same as:
Options:
A. 4% of a
B. 5% of a
C. 10% of a
D. 2% of a
Solution:  20% of a = b
= 4% of a that is Correct option: A