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## Percentage Problems

At the time of preparing for the Bank/SSC/UPSC/Railway etc examination it is must to have proper knowledge about the Percentage Problems and their solutions and shortcut tricks. In competitive examination it is must for candidates to maintain time. If time is properly managed then it will become very east for aspirants to solve the whole question paper in specified time limit.

Due to shortage of time mostly candidates skip the mathematical part. Keeping all these facts in mind here on this page of recruitmentresult.com we are providing some Percentage calculation shortcut tricks that will help you all in solving the Percentage Problems. These shortcut tricks cover all sorts of tricks on Percentage calculation. Candidates are advised to go through these shortcut tricks on percentage calculation very carefully and also wish them good luck for their further competitive examination.

### Percentage Problems

Concept of Percentage:

By a certain percent, we mean that many hundredths.

Thus, x percent means x hundredths, written as x%.

To express x% as a fraction: We have, x% = x/100                 .

Thus, 20% =  20/100 = 1/5

To express a/b as a percent: We have, a/b = (a/b x 100) %.

Thus, 1/4= (1/4 x 100)%

Percentage Increase/Decrease:

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

(R/(100+R) X 100)%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

(R/(100-R) X 100)%

Results on Population:

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

1. Population after n years = P X (1+ R/ 100)n
2. Population n years ago = P / (1+ R/ 100)n

Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

1. Value of the machine after n years = P X (1- R/ 100)n
2. Value of the machine n years ago = P/(1- R/ 100)n
3. If A is R% more than B, then B is less than A by = ((R/ (100 +R))x 100) %.
4. If A is R% less than B, then B is more than A by= ((R/ (100 – R))x 100) %.

Tricks & Shortcuts for Bank/SSC/UPSC/Railway

Percentage Problem is an essential chapter in Mathematics and it uses most chapters for calculation.Shortcut Tricks is based on, to find the number that is obtain in this type of questions. Just go through these Tricks and understand the easiest way of solving Percentage Problems. .

Percentage Shortcuts and Tricks:

1. Percent implies “for every hundred”.

% is read as percentage and x % is read as x per cent.

1. To calculate p % of y

(p/100) x y = (p x y)/100

p % of y = y % of p

1. To find what percentage of x is y: y/x × 100
2. To calculate percentage change in value

Percentage change = {change/(initial value)} x 100

1. Percentage point change = Difference of two percentage figures
2. Increase N by S % = N( 1+ S/100 )
3. Decrease N by S % = N (1 – S/100)
4. If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original point is 100x/ (100 + x) %.
5. If A is x% more /less than B, then B is 100x/(100 + x) % less/more than A.
6. If the price of an item goes up/down by x %, then the quantity consumed should be reduced by 100x/ (100 + x)% so that the total expenditure remains the same.

Check Out Here: Probability Questions With Answers

1. Successive Percentage Change

If there are successive percentage increases of a % and b%, the effective percentage increase is:

{(a + b + (ab/100)}%

1. Percentage – Ratio Equivalence:  N is Numerator

D is the Denominator

1. Product Stability Ratio:

A × B = P

If A is increased by a certain percentage, then B is required to be decreased by a certain percentage to keep the product P stable.

Expressing the percentage figures in ratios: 14. You Can Also Check: Maths Formulas

Some Percentage Problems along with Solutions:

Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

1. 39, 30
2. 41, 32
3. 42, 33
4. 43, 34

Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

1. 588 apples
2. 600 apples
3. 672 apples
4. 700 apples

Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?

1. 1
2. 14
3. 20
4. 21

Check Here: Problems on Ages Question & Answers

Question: If A = x% of y and B = y% of x, then which of the following is true?

1. A is smaller than B.
2. A is greater than B
3. Relationship between A and B cannot be determined.
4. If x is smaller than y, then A is greater than B.
5. None of these

Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is  of the number of students of 8 years of age which is 48. What is the total number of students in the school?

1. 72
2. 80
3. 120
4. 150
5. 100