# Tips And Tricks And Shortcuts of Percentage

## Tips ,Tricks and Shortcuts of Percentages

Percentages problems can be found in various fields, including mathematics, finance, and everyday situations. Whether you’re calculating discounts, tips, or interest rates, here are some tips and tricks and shortcuts of percentages to help you tackle percentage problems: ### Tips and tricks and shortcuts on Percentage

• Here, are quick and easy tips and tricks on PrepInsta page  for  Percentage problems swiftly, easily, and efficiently in competitive exams and other recruitment exams.
• If the value of an item goes up or down by x%, the percentage reduction or increment to be now made to bring it back to the original point is $\mathbf{\frac{x}{100 + x } × 100 }$ %
• If A is x% more or less than B, then B is $\mathbf{\frac{x}{100 + x } × 100 }$ %  less or more than A.
• If the price of an item goes up/down by x %, then the quantity consumed should be reduced by $\mathbf{\frac{x}{100 + x } × 100 }$ %  so that the total expenditure remains the same.
• Percentage – Ratio Equivalence table

Fraction Percentage

 $\frac{1}{3}$ × 100 = 33.33% $\frac{1}{10}$ × 100 = 10% $\frac{1}{4}$ × 100 = 25% $\frac{1}{11}$ × 100 = 9.09% $\frac{1}{5}$ × 100 = 20% $\frac{1}{12}$ × 100 = 8.33% $\frac{1}{6}$ × 100 = 16.66% $\frac{1}{13}$ × 100 = 7.69% $\frac{1}{7}$ × 100 = 14.28% $\frac{1}{14}$ × 100 = 7.14% $\frac{1}{8}$ × 100 = 12.5% $\frac{1}{15}$ × 100 = 6.66% $\frac{1}{9}$ × 100 = 11.11% $\frac{1}{16}$ × 100 = 6.25%

### 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)

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### Type 1: Percentage Tips and Tricks and Shortcuts- Based on Mixtures and Alligation

Question 1. 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 = $\frac{60 × 20 }{100}$ = $\frac{1200 }{100}$ = 12 litre

Let the water added = x

Now, $\frac{12 + x }{60 + x}$× 100 = 40 (it is because in the new mixture milk is 60%, 100 – 60 = 40% water)

1200 + 100x = 2400 + 40x

100x – 40x = 2400 – 1200

60x = 1200

x= 20 litre

Correct option: A

### Type 2: Percentage Tips and Tricks – Problems based on Ratios and Fractions

Question 1. If the numerator of a fraction is increased by 50% and the denominator is decreased by 10%, the value of the new fraction becomes $\frac{4}{5}$ . Find the original fraction?

Options:

A. $\frac{12}{21}$

B. $\frac{13}{20}$

C. $\frac{12}{25}$

D. $\frac{25}{12}$

Solution:     Let original numerator be x

Let original denominator be y

Let original fraction be $\frac{x}{y}$

According to the question,

Numerator of a fraction is increased by 50% = $\frac{150}{100x}$

Denominator is decreased by 10% = $\frac{90}{100}$

Now, $\frac{\frac{150}{100} x }{ \frac{90}{100} y}$= $\frac{4}{5}$

$\frac{150x}{90y}$ =$\frac{4}{5}$

$\frac{x}{y}$= $\frac{4}{5}$ × $\frac{90}{150}$= $\frac{12}{25}$

Correct option: C

### Type 3: Tips and Tricks and Shortcuts for Percentages-  Income, Salary, Expenditure

Question 1. 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

$\frac{60}{100}$x = 480

x = 480 × $\frac{100}{60}$

x = $\frac{48000}{60}$

x = 800

Therefore, his monthly salary = 800

Correct option: B

### Type 4: Percentage Tips and Tricks and Shortcuts- Problems based on Population

Question 1. 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 × $\frac{96}{100}$ = 2880

In the second year it increases by 5% = 2880 × $\frac{105}{100}$ = 3024

Correct option: A

### Type 5: Problems based on profit and loss

Question 1. 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

Question 1. 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

$\frac{20}{100}$ a = b

b% of 20 =$\frac{b}{100}$ × 20 = $\frac{20}{100}$ × $\frac{20}{100}$ × a

= 4% of a

Correct option: A

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### 3 comments on “Tips And Tricks And Shortcuts of Percentage”

• Chandra

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? provided solution is not understandable kindly solve it again using some other methord 67
• 16 0
• Prasanna

cp of 20 chairs=sp of x tables
20*cp = x*sp
sp/cp=20/x —>(1)
profit=25%
profit%formula,
p%= (sp-cp)/cp *100
25*100= (sp-cp)/cp
1/4=(sp-cp)/cp
1/4=(sp/cp)-1
thn from (1),
1/4=(20/x)-1
5/4=20/x
thus, x=16 6