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# Tips And Tricks And Shortcuts of Percentage

## Tips ,Tricks and Shortcuts of Percentages

Percentage is the  number expressed as a ratio multiplied by  100.. The symbol for the Percentage is  “% ” .It is also written as “per cent” . which means for every 100.

### 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%

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

$\frac{130x}{90y}$ =$\frac{4}{5}$

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

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

Now, $\frac{20}{100}[/latex] a × \frac{b}{100}$ × 20

= 4% of a

Correct option: A

Read Also - How to solve Percentage Problems Quickly

### One comment 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