Tricks to solve Percentage Problems - PDF

Percentage is a fraction whose denominator is always 100. x percentage is represented by x%.

Calculation of Percentage

If we have to find y% of x, then

1. To express x% as a fraction : 

We know

x% = ^x/100

Thus 10% = ¹⁰/100 (means 10 parts out of 100 parts)

= ¹/10 (means 1 part out of 10 parts)

2. To express x/y as a percentage :

We know that ^x/y  = (^x/y× 100 )

Thus ¹/4 = ( ¹/4 ×100 )% = 25%

and 0.8 = ( ⁸/10 ×100 )% = 80%

3. To increase a number by a given percentage(x%): 

Multiply the number by the following factor

4. To decrease a number by a given percentage(x%): 

Multiply the number by the following factor

5. To find the % increase of a number:

6. To find the % decrease of a number:

Some Observation

#1 

If 20% candidate failed in an exam then observations are

• 80% represent passed in exam
• 100% represent total appeared in exam
• (80%-20%) = 60% represent difference between passed and failed candidate in exam

#2

 If a number is increased by 25% then observations are 

• 100% represent the old number
• 125% represent the new number.

#3

 Remember that Base in the given sentence (Question) is always 100%

Eg. Income of Ram is increased by 20% 

In this sentence 

100% - represent the income of Ram

20% - represent increment

120% - represent new income of Ram.

Remember it :

1 = 100%

1/2 = 50%

1/3 = 33 1/3%

1/4 = 25%

1/5 = 20%

1/6 = 16²/3%

1/7 = 14²/7%

1/8 = 12¹/2%

1/9 = 11¹/3%

1/10 = 10%

1/11 = 9¹/11%

1/10 = 8¹/3%

1/13% = 7⁹/13%

25% = 1/4

6.25% = 1/16

125% = 5/4

150% = 3/2

200% = 2

350% = 7/2

#4

If of A is equal to y% of B then -

Example: - If 10% of A is equal to 12% of B, then 15% of A is equal to what percent of B?

#5

If A is more than B,

Example: - If income of Ravi is 20% more than that of Ram, then the income of Ram is how much percent less than that of Ravi?

#6

If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then–

Example: - Pankaj Sharma has to score 40% marks to get through. If he gets 40 marks and fails by 40, then find the total marks set for the examination?

#7

If a candidate scores marks and fails by a marks while an another candidate scores y% marks and gets b marks more than minimum passing marks, then –

Example: - Raj scores 30% and fails by 60 marks, while Rohan who scores 55% marks, gets 40 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination?

#8

If due to decrement in the price of an item, a person can buy Kg more in y rupees, then actual price of that item -

Example: - Ram can buy 5 Kg more sugar in rupees 100 as the price of sugar has decreased by 10%. Find the actual price of the sugar?

#9

If in an election, a candidate got of total votes cast and still lose by y votes, the total number of votes cast –

Example: - In an election contested by two candidates, one candidate got 40% of total votes and still lost by 500 votes, find the total number of votes casted?

#10

If the population of a town is P and it increases or decreases at the rate of R% per annum then –
I. Population after ‘n’ years :

II. Population ‘n’ years ago :

Example: - The population of a town is 352800. If it increases at the rate of 5% per annum, then what will be its population after 2 years and 2 years ago?

#11

If the value of a number is first increased by and again decreased by the net effect is always decreased by ^x2/₁₀₀%
Example: -The salary of a worker is first increased by 5% and then it is decreased by 5%. What is the change in his salary?

Examples

#1 

Q. If the difference between 62% of a number and 3/5th of that number is 36. what is the number ?

Sol:

Let the number be x.

Then x × 62% - x × ³/5 = 36

x ×62% -x V 60% = 36 (60% = 3/5)

x ×2% = 36

x ×²/100 =36

x = ^36 ×100/2 = 1800

#2

Q. 40% of Ram's income Rs. 1200 Then Find 

1. 75% of Ram's income ?
2. 1/4 part of Ram's income ?
3. 1/3 part of Ram's income ?

Sol :

(1)

40% = 1200 Rs.

75% = 1200/40 ×75 = 2250 Rs.

Trick : 1200 / 40  × 75 = Rs. 2250/-

(2)

40% of income = Rs. 1200

Then 1/4 part (i.e. 25% ) of Ram's

income = 1200/40 ×25 

= Rs. 750/- Ans

(3)

40% of Ram's income

= Rs. 1200

i.e. 2/5 part of Ram's income

= Rs. 1200

Then total income of Ram 

= Rs. 1200 ×5/2

1/3 part of Ram's income

= Rs. 1200  × ⁵/2  × ¹/3 

= Rs. 1000 Ans.

Trick :

¹²⁰⁰/_2/5  × 1/3

= ¹²⁰⁰/2 × ⁵/3 = 1000

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