Percentage

Percentage

Percentage is a way of expressing a number as a fraction of 100.

i.e. per cent means per hundred (means that number divided by 100)

It is denoted as ‘%’.

Tricks to solve the Percentage Problems

·         For converting a fraction and a decimal to a percentage, multiply by 100 (Calculation of percentage means multiplying 100).

·         For converting a percentage to a fraction and a decimal, divide by 100 (Given percentage is converted into normal form means divide by 100).

Examples

1.      56% = 56/100 = 0.56 (percentage converted into decimal form)

2.      27/4 = (27/4) × 100 = 675% (decimal or fraction converted into percentage)

3.      0.004 = 4/1000 = (4/1000) × 100 = 0.4%

4.      6% = 6/100 = 0.06

Evaluate :-

1.      28% of 450 + 45% of 280 = ?

Solution:

                  (28/100) × 450 + (45/100) ×280 = 126 + 126 = 452 (Ans.)

2.      What percentage of 2.75 is 25 ?

Solution:

                  Required percentage = (25/2.75) × 100 =9.09%

For beginners;

x% of 2.75 = 25

(x/100) × 2.75 = 25

On calculation, x=9.09% 

3.      2 is what percent of 50 ?

Solution:

                  Required percentage = (2/50) × 100 = 4%

Percentage of increase and decrease in between two quantities

Let two quantities be x and y

·         Then, x is m% more than y, then y is less than x by [(m/100+m) × 100]%

·         x is m% less than y, then y is more than x by [(m/100−m) × 100]%

Results on Population

Let the population of a town be A now and it increases at rate of m% per annum, then :

•     Population after n years = A [1 + (m/100)]ⁿ  

•     Population before n years = A/ [1 + (m/100)]ⁿ 

Miscellaneous Examples

1.  Which is greatest in 50/3 %, 0.17 & 2/15 .

Solution:

      Take all into the same form as decimal form, so that you can get greatest among these.

       50/3 % = (50/3 )× (1/100) = 1/6 = 0.166 , 2/15 = 0.133

      Clearly from above, 0.17 is the greatest.

2. A student multiplied a number by 3/5 instead of 5/3 . Find the error percentage.

Solution:

       Let the number be x.

      Then, the error = (5/3) x – (3/5) x = (16/15)x

      Error percentage =  [(16/15)x / (5/3) x ] × 100 = 64%

(Tricks- compare always with base part & base be at denominator always)

 

3.  What percent of a day is 3 hours ?

Solution:

                 Required percentage =  [(3/24 )×100]% = (25/2)% = 12.5%

 

4.  A’s income is 25% more than B’s income. Find B’s income in terms of A’s income.

Solution:

A = 125% of B ⟹ A = (125/100)B ⟹ B = [(100/125) × 100]% of A = 80% of A

 

5.  A’s salary is 50% more than B’s. How much percent is B’s salary less than A’s?

      Solution:

                  Required answer =[(50/150) × 100]%  = (100/3)%

 

6.  The difference of two numbers is 20% of the larger number. If the smaller number is 20, find the larger number.

Solution:

                  Let two numbers be a & b and a > b

                  Then a – b = 20% × a = a/5 ⟹ a – (a/5) = b = 20 ⟹ a = 25

 

7. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is :

Solution:

Percentage increase in 10 years (decade) =

 [(262500 – 175000) / 175000] × 100 %  =50%

Required average = (50/10)% = 5%

 

8. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. Find the maximum marks.

Solution:

                  Pass mark = 125 + 40 = 165

                  If    33% = 165

                     ⟹ 100% = (165/33) × 100 = 500 (Full marks)

 

9. In an examination, 35% of the students passed and 455 failed. How many students appeared for the examination?

Solution:

                  Let total students appeared be x

                  Passed = 35% and failed = 65%

                  65% of x = 455 ⟹ x = 700 (Ans.)

 

10.  If  50% of (x − y) = 30% of (x + y), then what percent of x is y ?

Solution:

                  50% of (x − y) = 30% of (x + y)

⟹ 5 (x − y) = 3 (x + y) ⟹ x = 4y

Required percentage = [(y/x) × 100] %  = [(y/4y) × 100]%  = 25%                      

Do it yourself

1. The salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary ? (Ans. 100/9 %)

2. If the numerator of a fraction be increased by 15% and its denominator be decreased by 8%, the value of the fraction is (15/16). Find the original fraction. (Ans. 3/4)

3. If one number is 80% of the other & 4 times the sum of their squares is 656, then the numbers are : (Ans.10, 8)

4. If x% of a is the same as y% of b, then z% of b is : (Ans. xz/y % of a)

5. A housewife saved Rs.2.50 in buying an item on sale. If she spent Rs.25 for the item, approximately how much percent she saved in the transaction ? (Ans.9%)

6. If a number is increased by 25% and then decreased by 25%, find out the percentage of increase/decrease of the final value of the number ?

7. If 60% of 5/12 of a number is 9.5, then find out the number?

8. A invested 20% more than B, B invested 25% less than C. If the total sum of their investment is Rs.2650, how much amount did B invest?

Previous Years Questions 

1. If the given numbers are respectively 6% & 24% of a third number,  then what percentage is the first number of the second number?

2. The difference of two numbers is 25% of the greatest number.  If the smaller number is 30. What is greatest number?

3. In an election of two candidates who gets 41% is defeated by a margin of 2412 votes.  Find the total number of votes? (Ans. 13400)

4. A candidate who gets 20% marks in an examination,  fails by 30 marks. But, if he gets 32% marks, he gets 42 marks more than the minimum pass marks. Find the pass percentage of marks ?

5. How much 200/3 % of Rs.312 exceeds Rs.200? 

6. The population of a town is decreasing at a rate of 10% p.a. If the population 2 years ago was 20,000, then what is the present population?

7. Anil's salary was Rs.18,000. An increase of 20% each in two consecutive years is equal to a single increment of what percentage?

8. Sachin scored a century which included 3 fours and 8 sixes. As a result, what percentage of his total score did Sachin score by running between the wickets?