Shortcut tricks for percentage

What is the meaning of percentage  

Percentage also known as PCT in short-form. Before directly jumping into the shortcut tricks for percentage. Let’s first understand what is the meaning of percentage. The percent is made of two words Per and cent, Per means “every” and cent means “hundred”. It means how many of some things are there in 100.

For example, If a student gets 5 marks out of 10, he gets 50 percent of marks. This can be understood by a logic that if the same exam would have been of 100 marks then the student had gotten 50 marks that is why we are saying that he has got 50% of marks.

To convert in percentage, we multiply the fraction by 100.

For example, if the student has got 5 out of 10 marks, in fraction it can be written as 5/10.

Now to convert fraction into percentage multiply fraction by 100, 
(5/10) * 100 = 50 %

 Percentage shortcut tricks

  • 1% of a number means 1/100 or 0.01 of that number
  • 10% of a number means 10/100 or 0.1 of that number
  • 50% of a number means 50/100 or just half of that number
  • 100 % of a number means 100/100 of that number that is the number itself
  • 200 % of a number means 200/100 of that number that is twice of the number
  • 0.1   % of a number means 0.1/100 of that number, in decimal 0.001 of that number
  • Now if we want to know the 5 % of a number simply calculate 10% and divide that by 2
  • If we want to know 2% of a number just find 1% and twice it
  • If we want to know 20% of a number find 10% and multiply it by 2
  • Similarly, 30% of a number find 10% and multiply it by 3

Percentage shortcut tricks

Examples :

Find 59 % of 45

59% of 45 = 50% of 45 + 10% of 45 -1% of 45
= 22.5 + 4.5 – 0.45 = 26.55

By doing the above method calculation becomes too easy and it can be easily calculated without pen and paper.

 Find 27 % of 68:

27 % of 68 = 10% of 68 + 10% of 68 + 5% of 68 + 1% of 68 + 1% of 68 =
= 6.8 + 6.8 + 3.4 + 0.68 + 0.68=
= 13.6 + 3.4 + 1.36 = 18.36

Find 15.5 % of 1465

15.5 % of 1465 = 10 % of 1465 + 5% of 1465 + 0.5% of 1465
= 146.5 + 73.25 + 7.325 = 227.075

Related topics: tricks and shortcuts for squaring and multiplication.

Important formulas and shortcut tricks for percentage:

Percentage profit formula: 

    \[ Percentage\enspace profit=\]

    \[ = \frac{Profit * 100} {C.P.} \]

    \[ = \frac{(S.P.-C.P.) * 100} {C.P.} \]

Where, S.P. = Selling price
C.P. = Cost price

Example 1: A mobile phone is purchased for Rs. 4500 and sold for 5000. Find the gain or profit percent.
Answer:

    \[ Percentage\enspace profit=\]

    \[ = \frac{(S.P.-C.P.) * 100} {C.P.} \]

    \[ = \frac{(5000-4500) * 100} {4500} \]

    \[ = \frac{(500) * 100} {4500} \]

    \[ = \frac{100} {9} = 11.11 \enspace Percent\]

Percentage loss formula: 

    \[ Percentage\enspace loss =\]

    \[ = \frac{Loss * 100} {C.P.} \]

    \[ = \frac{(C.P.-S.P.) * 100} {C.P.} \]

 

Example 2:  A scooter is sold for Rs. 50000 at a loss of 20 percent. Find the cost price of the scooter.
Answer:

    \[ Percentage\enspace loss =\]

    \[ = \frac{(C.P.-S.P.) * 100} {C.P.} \]

    \[ =20 = \frac{(C.P.-50000) * 100} {C.P.} \]

    \[ =0.2 = \frac{(C.P.-50000)} {C.P.} \]

    \[ =0.8 C.P. = 50000\]

    \[ =C.P. = \frac{50000}{0.8} = 62500\]

 Percentage error formula:

    \[ Percentage \enspace error =\]

    \[\frac{|Exact \enspace value - Exp. \enspace  value| * 100 }{|Exact \enspace value|}\]

Exp. value means experimental value.

Example 3: The forecasted rain was 10 mm but actually it turned out to be 15 mm. Find percentage error in forecasting.
Answer:

    \[ Percentage \enspace error =\]

    \[\frac{|Exact \enspace value - Exp. \enspace  value| * 100 }{|Exact \enspace value|}\]

    \[\frac{|15 - 10| * 100 }{|15|}\]

    \[\frac{5 * 100 }{15}= 33.33 \enspace  percent\]

Percentage decrease in consumption formula: 

The price of a commodity is increased by P%, than the percentage reduction in consumption, if the expenditure is the same as before.

    \[ Percent.\enspace dec. \enspace in \enspace consumption =\]

    \[= \frac { P * 100}{100+P}\]

Example 4: If the price of sugar is increased by 25%, by what percentage a family must reduce the consumption of sugar, so that expenditure remains same ?

Answer:

    \[ Percent.\enspace dec. \enspace in \enspace consumption =\]

    \[= \frac { P * 100}{100+P}\]

    \[= \frac { 25 * 100}{100+25} = 20 \enspace percent \]

Percentage Increase in consumption formula

If the price of a commodity is decreased by P%, then the percentage increase in consumption, if the expenditure is the same as before

    \[ Percent.\enspace Inc. \enspace in \enspace consumption =\]

    \[= \frac { P * 100}{100-P}\]

Example 5: Divyansh spends Rs 600 on vegetables every month. The price of vegetables is decreased by 20% and he is able to buy 5 kg more vegetables. What was the original price of the vegetable ( per kg) ?

Answer: Let Divyansh used to buy ‘x’ kg before.
Percentage increase in consumption = (5 *100)/x

    \[ Percent.\enspace Inc. \enspace in \enspace consumption =\]

    \[= \frac { P * 100}{100-P}\]

    \[ =\frac{5 *100}{x}=\frac { 20 * 100}{100-20}\]

    \[ =\frac{500}{x}=\frac { 20 * 100}{80}\]

    \[ =\frac{500}{x}=25\]

    \[ =x=\frac{500}{25}= 20\]

So, earlier he used to buy 20 kg vegetables at Rs. 600.
So, earlier price of 1 Kg vegetable = 600/20 = Rs. 30

If a number is successively increased by X % and then Y %,

Then effective percentage change =

    \[ (X + Y + \frac {X*Y}{100}) \]

Population after and before “T” Years

Let the current population of a town is P now and it increases at an at the rate of R% than

Total population after ‘T’ years =

    \[ = P * ( 1 + (R / 100)^T\]


Total population before “T” years

    \[ =\frac {P} { ( 1 + (R / 100)^T}\]

Percentage change formula:

Find the % change if a number ‘A is changed to ‘B’

    \[Percentage \enspace change =\]

    \[ =\frac{Change \enspace in \enspace value \enspace of \enspace no.}{ original \enspace no.}*100\]

    \[ = \frac{ B - A} {A} * 100\]

 

 If X is P% more than Y, then Y is less than X by what percentage:

    \[= \frac { P}{100+P}*100\]

If X is P% less than Y, then Y is more than X by what percentage:

    \[= \frac { P}{100-P}*100\]

Also know: how to calculate the number of rectangles and square in a grid

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