Important Formula: Percentages

# Important Formula: Percentages | Quantitative Aptitude for SSC CGL PDF Download

## Percentage Formula

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

## Formulas for Percentages & Definitions

• In mathematics, a percentage is a number or ratio expressed as a fraction whose denominator (bottom) is 100. Thus, x percent means x hundredths, written as x%.
We express x% as a fraction as x/100.
• For example 10% = 10/100 = 1/10

## Percentages Difference Formula

• When provided with two values and tasked with determining the percentage difference between them, this can be accomplished using the following formula:

### Formulas & Basic Concept of Percentages

• To calculate a % of b
• To find what percentage of a is b
• To calculate percentage change in value
Percentage change
• Percentage Increase or Decrease
• Percentage increase
• Percentage decrease
• Successive Percentage Change

If there are successive percentage increases of a % and b%, the effective percentage increase is:

• Results on population:
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

• Population after n years

• Population n years ago

• Results on Depreciation:
Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

• Value of the machine after n years

• Value of the machine n years ago

• If A is R% more than B, then B is less than A by

• If A is R% less than B, then B is more than A by

• Increase N by S% :

• Decrease N by S%:

Q1: Peaches are now 50% more expensive at Reliance Smart Point. What percentage reduction in consumption is required to maintain peach expenditure constant?
(a) 35 %
(b) 35.50 %
(c) 33.33 %
(d) 32.50 %
Ans:
(c)
If the price of a commodity increases by r%, then the reduction in consumption so as not to increase the expenditure is –

Therefore r is the increased price(i.e 50)
By using the formula:

Q2: To pass the NDA Recruitment Test, candidates must receive 290 of the aggregate marks to pass. What is the highest total of marks an applicant can receive if they receive 203 and are considered unsuccessful by 12% of their total scores?
(a) 750
(b) 725
(c) 700
(d) 675
Ans:
(b)
Let’s maximum aggregate marks = x
203 + 12% of x = 290
12% of x = 290 – 203

Q3: If Yasir’s income is 20% less than Xavier’s, by what percentage does Yasir’s salary fall short of Xavier’s?
(a) 16.66 %
(b) 15.50 %
(c) 14.45 %
(d) 13.45 %
Ans:
(a)
Let the salary of Yasir be 100. then,
Salary of Xavier will be 120.
Yasir less than Xavier in %,

Q4: Jason Statham could set aside 10% of his earnings. However, when his income increased by 20% two years later, he could only save the same amount as before. How much has his spending increased by percentage?
(a)
(b)
(c)
(d)
Ans:
(a)
Let earlier income be 100 Rs
∴ Savings = 10% of 100 = 10 Rs
∴ Expenditure = 90 Rs
New Income = 120 Rs
Savings (same as before) = 10 Rs
∴ Expenditure = 120 – 10 = 110 Rs
∴ Increase in Expenditure = 110 – 90 = 20

Q5: Robert Pattinson is an IT professional who spends 12% of his monthly income on power, 25% of his income on food, 20% of his income on his children’s education, 30% of his income on rent, and the rest 1040 on everything else. What is the person’s monthly salary?
(a) 7500 Rs
(b) 7700 Rs
(c) 7900 Rs
(d) 8000 Rs
Ans:
(d)
Let the monthly salary of the Robert be x. then,
Total spends of Robert = (30 + 25 + 20 + 12) = 87%
Remaining % = 100 – 87 = 13%
So, 13% ≡ 1040
100% ≡ x
Using the cross multiplication method,

The document Important Formula: Percentages | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
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## Quantitative Aptitude for SSC CGL

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## FAQs on Important Formula: Percentages - Quantitative Aptitude for SSC CGL

 1. What is the formula for calculating percentages?
Ans. The formula for calculating percentages is: (Part/Whole) x 100. This formula is used to find the percentage value of a part in relation to the whole.
 2. What are some important formulas related to percentages?
Ans. Some important formulas related to percentages include: - Percent Increase/Decrease: ((New Value - Old Value) / Old Value) x 100 - Percentage Change: ((Final Value - Initial Value) / Initial Value) x 100 - Percent of a Number: (Percentage/100) x Number - Percentage Increase: (Increase/Original Number) x 100 - Percentage Decrease: (Decrease/Original Number) x 100
 3. How is the percentage difference calculated?
Ans. The percentage difference is calculated using the formula: ((New Value - Old Value) / Old Value) x 100. This formula helps in determining the percentage difference between two values, indicating the increase or decrease in value.
 4. How can percentages be useful in real-life situations?
Ans. Percentages are useful in various real-life situations, including: - Calculating discounts during sales or promotions. - Determining the percentage of marks obtained in exams. - Analyzing population growth or decline rates. - Calculating interest rates on loans or investments. - Comparing prices to find the best deal.
 5. What does the term "percentages" mean?
Ans. The term "percentages" refers to a way of expressing a fraction or a part of a whole in terms of hundredths. It represents a proportion or a ratio out of 100. Percentages are commonly used to compare quantities, express growth or decline rates, and interpret statistical data.

## Quantitative Aptitude for SSC CGL

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