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 of Percentage

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{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


    • 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