Percentages Concept,Formulas,TIps,Tricks,Problems with solutions

What is percentage:

The word percent can be understood as follows:

Per cent => for every 100.

So, when percentage is calculated for any value, it means that that you calculate the value for every 100 of the reference value

Why Percentages:

Percentage is a concept evolved so that there can be a uniform platform for comparison of various things. (Since each value is taken to a common platform of 100.)

Eg: To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another.

Basic tips for faster calculations:

Calculation of Percentage:

Percentage = (Value / Total value) X 100

Eg: 50 is what % of 200?

Soln: Percentage = (50/200) X 100 = 25%.

Calculation of Value:

Value = (Percentage/100) X total value

Eg: What is 20% of 200?

Soln: Value = (20/100) X 200

Note: Percentage is denoted by “%”, which means “/100”.

Eg: What is the decimal notation for 35%?

Soln: 35% = 35/100 = 0.35.

For faster calculations we can convert the percentages or decimal equivalents into their respective fraction notations.

Conversions:

Percentages – Fractions Conversions:

The following is a table showing the conversions of percentages and decimals into fractions:

Percentage Decimal Fraction

10%                            0.1                               1/10

12.5%                         0.125                           1/8

16.66%                       0.1666                         1/6

20%                            0.2                               1/5

25%                            0.25                             1/4

30%                            0.3                               3/10

33.33%                       0.3333                         1/3

40%                            0.4                               2/5

50%                            0.5                               1/2

60%                            0.6                               3/5

62.5%                         0.625                           5/8

66.66%                       0.6666                         2/3

70%                            0.7                               7/10

75%                            0.75                             3/4

80%                            0.8                               4/5

83.33%                       0.8333                         5/6

90%                            0.9                               9/10

100%                          1.0                                1

We will see how use of fractions will reduce the time for calculations:

Eg: What is 62.5% of 320?

Soln: Value = (5/8) X 320 (since 62.5% = 5/8)

= 200.

Percent change:

A change can be of two types – an increase or a decrease.

When a value is changed from initial value to a final value,

% change = (Difference between initial and final value/initial value) X 100

Eg: If 20 changes to 40, what is the % increase?

Soln: % increase = (40-20)/20 X 100 = 100%.

Note:

1. If a value is doubled the percentage increase is 100.
2. If a value is tripled, the percentage change is 200 and so on.
3. Percentage Difference:

% Difference = (Difference between values/value compared with) X 100.

Eg: By what percent is 40 more than 30?

Soln: % difference = (40-30)/30 X 100 = 33.33%

(Here 40 is compared with 30. So 30 is taken as denominator)

Eg: By what % is 60 more than 30?

Soln: % difference = (60-30)/30 X 100 = 100%.

(Here is 60 is compared with 30.)

Hint: To calculate percentage difference the value that occurs after the word “than” in the question can directly be used as the denominator in the formula.

Important Points to Note:

1. When any value increases by
1. 10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)
2. 20%, it becomes 1.2 times of itself.
3. 36%, it becomes 1.36 times of itself.
4. 4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

1. When any value decreases by
1. 10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)
2. 20%, it becomes 0.8 times of itself
3. 36%, it becomes 0.64 times of itself
4. 4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

Note:

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on.

Eg: When the actual value is x, find the value when it is 30% decreased.

Soln: 30% decrease => 0.7 x.

Eg: A value after an increase of 20% became 600. What is the value?

Soln: 1.2x = 600 (since 20% increase)

ð     x = 500.

Eg: If 600 is decrease by 20%, what is the new value?

Soln: new value = 0.8 X 600 = 480. (Since 20% decrease)

Thus depending on the decimal we can decide the % change and vice versa.

Eg: When a value is increased by 20%, by what percent should it be reduced to get the actual value?

Soln: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula)

% decrease = (1.2 – 1)/1.2 X 100 = 16.66%.

1. When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes.

Eg: The population of a town increased by 10%, 20% and then decreased by 30%. The new population is what % of the original?

Soln: The overall effect = 1.1 X 1.2 X 0.7   (Since 10%, 20% increase and 30% decrease)

= 0.924 = 92.4%.

Eg: Two successive discounts of 10% and 20% are equal to a single discount of ___

Soln: Discount is same as decrease of price.

So, decrease = 0.9 X 0.8 = 0.72 => 28% decrease (Since only 72% is remaining)

Percentages problems with solutions:

Exercise:

1. If 20% of 40% of a = 25% of a% of b, then what is b?

a. 8/5               b. 16/25                       c. 8/25             d. None

2. By what % is 200 more than 50?

a. 100              b. 200                          c. 300              d. None

3. A value changes from 30 to 80. What is the percentage change?

a. 125              b. 166.66                     c. 156              d. None

4. The population of a city is increased by 30% and thus became 78000. What is the original population?

a. 76000          b. 64200                      c. 60000          d. None

5. In a theatre, the number of seats is increased by 20% and the price per ticket is increased by 10% but the public response decreased by 30%. What is the net effect on the economy of the theatre?

a.10% rise        b. 7% fall                      c. 7% rise         d. None

6. A saves 20% of his income. His income is increased by 20% and so he increased his expenditure by 30%. What is the percentage change in his savings?

a. 20% fall        b. 4% fall                      c. 20% rise       d. 4% rise

7. The price of petrol is increased by 25%. By what percent the consumption be reduced to make the expenditure remain the same?

a. 25%             b. 33.33%                    c. 20%             d. None

8. The side of a square is increased by 20%. The percentage change in its area is ___

a. 20%             b. 44%                         c. 36%             d. None

9. If the length of a rectangle is increased by 33.33%, by what percentage should the breadth be reduced to make the area same?

a. 20%             b. 33.33%                    c. 25%             d. None

10. In an election between two candidates, A and B, A secured 56% of the votes and won by 48000 votes. Find the total number of votes polled if 20% of the votes were declared invalid.

a. 500000        b. 400000                    c. 600000        d. None

11. A reduction of 10% in price of sugar enables a housewife to buy 5 kg more for Rs. 300/-. Find the reduced price per kg of sugar.

a. 5/-                b. 4.5/-                         c. 6/-                d. None

12. From a 20lt solution of alt and water with 20% salt, 2lt of water is evaporated. Find the new % concentration of salt.

a. 20%             b. 23%                         c. 25%             d. None

13. In a list of weights of candidates appearing for police selections, the weight of A is marked as 58 kg instead of 46.4 kg. Find the percentage of correction required.

a. 30                b. 20                            c. 24                d. None

14. A person spends 20% of his income on rent, 20% of the rest on food, 10% of the remaining on clothes and 10% on groceries. If he is left with Rs. 9520/- find his income.

a. 10000/-                    b. 15000/-                    c. 20000/-        d. None

15. A shopkeeper offers three successive discounts of 10%, 20% and 30% to a customer. If the actual price of the item is Rs. 10000, find the price the custome has to pay to the shopkeeper.

a. 5040/-                      b. 4000/-                      c. 6000/-          d. None

16. If  10lt solution of water and alcohol containing 10% alcohol is to be made 20% alcohol solution, find the volume of alcohol to be added.

a. 1 lt                            b. 1.25 lt                      c. 1.5 lt             d. 2 lt

17. A is twice B and B is 200% more than C. By what percent is A more than C?

a. 400                          b. 600                          c. 500              d. 200

18. In an examination, a student secures 40% and fails by 10 marks. If he scored 50%, he would pass by 15 marks. Find the minimum marks required to pass the exam.

a. 250                          b. 100                          c. 110              d. 125

19. If A is 20% taller than B, by what percent is B shorter than A?

a. 20%                         b. 25%                         c. 16.66%        d. None

20. The population of a town increases at a rate of 10% for every year. If the present population is 12100, find the population two years ago.

a. 11000                      b. 9800                        c. 10000          d. 10120

21. A solution of salt and water contains 15% salt. If 30 lt water is evaporated from the solution the concentration becomes 20% salt. Find the original volume of the liquid before water evaporated.

a. 100 lt                        b. 120 lt                       c. 200 lt            d. None

22. If 240 lt of oil is poured into a tank, it is still 20% empty. How much more oil is to be poured to fill the tank?

a. 300 lt                        b. 60 lt                         c. 120 lt            d. None

23. A and B were hired for the same salary. A got two 40% hikes whereas B got a 90% hike. What is the percentage difference in the hikes thay got?

a. 16%                         b. 6%                           c. 10%             d. 8%

24. The population of a town doubled every 5 years from 1960 to 1975. What is the percentage increase in population in this period?

a. 800                          b. 400              c. 700              d. 600

25. In a test of 80 questions, Jyothsna answered 75% of the first 60 questions correctly. What % of the remaining questions she has to answer correctly so that she can secure an overall percentage of 80 in the test?

a. 80%                         b. 90%             c. 85%             D. 95%

Solutions:

1. 1/5 X 2/5 X a = ¼ X a X b  =>  b = 8/25
2. % difference = (200-50)/50 X 100 = 300 %
3. % increase = (80-30)/30 X 100 = 166.66 %
4. 1.3 x = 78000  =>  x = 60000.
5. Net effect = 1.2 X 1.1 X 0.7

= 0.924  =>  7.6% decrease.

1. Let I be the income.

Expenditure = 0.8I                 Savings = 0.2I => 20%

New income = 1.2I  (since 20% rise)

New expenditure = (0.8I) X 1.3  (Since 30% rise)

= 1.04I

So, new savings = 1.2I – 1.04I = 0.16I => 16%

(So income decreased form 20% to 16%)

% decrease = (20-16)/20 X 100 = 20%.

1. It is equivalent to 1.25 decreased to 1.

% decrease = (1.25-1)/1.25 X 100 = 20%

8. % change in area = 1.2 X 1.2 (since area = side X side)

= 1.44 => 44%.

1. It is equivalent to 1.25 decreased to 1. So 20% decrease.

A got 56%  =>  B got 44%

Difference = 12% = 48000

So, 100% = 400000. These are valid votes.

So, 80% of total votes  = 400000  =>  total votes = 500000

1. Total money = Rs. 300.

Saving of the lady = 10% of 300 = 30/-

With 30/- she bought 5 kg sugar => each kg costs Rs. 6/-

1. In 20lt, salt = 20% => 4 lt.

New volume = 18 lt (2 lt evaporated)

So, new % = 4/18 X 100 = 22.22%

1. % correction = (58-46.4)/58 X 100 = 20%
2. Three successive decreases of 20%, 20% and 10% => 0.8 X 0.8 X 0.9 = 0.576

Again 10% decrease => 0.576 – 0.1 = 0.476.

So, 0.476 x = 9520 => x = 20000.

1. Total discount = 0.9 X 0.8 X 0.7 = 0.504 of actual price.

So, price = 0.504 X 10000 = 5040.

1. In 10 lt, alcohol is 10% = 1 lt.

Let x lt alcohol is added.

So, (1+x)/(10+x) = 20% = 1/5  =>  x = 1.25 lt.

1. A = 2B and B = 3C (ince 200% more)

ð     A = 6C  =>  500 % more.

1. 50% of max marks – 40% of max marks = 25

ð     max marks = 250

Pass marks = 40% of max + 10 => 100 + 10 = 110.

1. A = 1.2 B => B = A/1.2 => 0.8333A => 16.66%.

(OR) Decrease from 1.2 to 1 => 16.66%.

1. 1.1 X 1.1 X x = 12100 => x = 10000.
2. Salt = 15% of x = 0.15x (x = volume of solution)

Now, 0.15x/(x-30) = 20% = 1/5  (since 30 lt evaporated)

ð     x = 120 lt

1. 20% empty => 80 % full = 240 lt  => 20% = 60 lt
2. A => 1.4 X 1.4 = 1.96

B => 1.9      => 6% difference.

24. From 1960 to 1975, in 15 years population doubled every 5 yrs => three times

So, 2 X 2 X 2 = 8 times => 700% more.

1. [(75% X 60) + (x% X 20)] / 80 = 80%  =>  x = 95.   (since required is 80%)

(OR)  60 out of 80 is 3/4. So,  (3/4 X 75)  +  (1/4 X x)  = 80  =>  x =95.

The main concepts along with examples and exercise problems with solutions explained clearly.If you really have interest to Attempt ibps exam seriously,have it ,understand the concept, You can crack the problems on percentages in your final exam.

1. manik rao karanam :

It’s really vry good n i m thankful to evry1 behind dis work

2. mounika :

• Syed :

thanks Mounika,you can follow these percentages tips while solving the problems,you will not get all these short tricks any books,we are very happy for using these tricks to save time in any exam

3. mohan :

Very good content.. thanks. it helped me a lot

4. Saranya :

Thanks a lot,.It is very helpfull…..

5. manjusha k k :

thanks sir,
sir i would like to introduce one tip to find out the square of numbers from 10 to 100.
suppose we want to find out square of the number ‘ab’ ,in which ‘a’ is in 10 nth place and ‘b’ is in ones place. If the square of this number is xyz. To find this please go through the following steps
step1: In ‘xyz’ z= b*b;
step 2: y= carry from step1+2*a*b;
step 3: z=carry from step2 + b*b;

Eg: to find the square of 32
step 1: 2*2=4 is in ones place of the answer
step 2: 2*3*2=12 , in 12 , 2 goes to the tenth place 1 is carry for the 100dth place.
step 3: 3*3+ carry from step 2 ,ie 10
ie 32*32 = 1024

• Syed :

Thanks Manjusha,this is really helpful for all

• manjusha k k :

sorry sir,
step 3 is wrong . Actually i mean
step 3: carry from step2+ suare of ‘ a ‘ ie a * a;
sir i kindly request to u that , if u think this tip is really helpful to others, please modify this in to a form that is easily captured to others.

• ashu :

thanx manjushaa 🙂

6. surekha :

thank u sir
it is very helpful to everyone

7. prasanna :

Sir,
I think 10th answer procedure is wrong at the final step..100% of votes is 400000 but in the qustion we require nly valid votes so 80% of total votes is 320000..but how do u get 500000…could anyone pls help me out..

8. prasanna :

Sir,

I think 13th solution is also wrong…error % = true value-false value/true value*100…so the answer is 25%

9. Prabhu :

It’s really very very helpful for to all

10. satish :

yes i agree with u mam

11. satish :

s i agree with u

• satish :

i is very help full and use full in daily life

12. Kaustav Ghosh :

a person secured 62% of votes in a poll won by 144 votes more. what is the total no of votes polled??

13. priya chanderiya :

hindi me question nahi milenge kya

14. Anurag Mishra :

its so good and very helpful for everybody.

15. manjula :

in exercise solution1 a represented with percentage and in answer the calculation done without percentage kindly modify

• rama krishna :

rama krishna:thank you very much .its really too good.