Tips And Tricks And Shortcuts of Percentage

July 17, 2020

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

SP of x table = 20

Profit = Rs. 20 – x

Therefore, $\frac{20 – x}{x} × 100$ =

2000 – 100x = 25x

2000 = 25x + 100x

2000 = 125x

x = $\frac{2000}{125}$

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, $\frac{20}{100}[/latex<strong>]</strong> a × \frac{b}{100}$ × 20

= 4% of a

Correct option: A

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

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