## Percentage Formula and Shortcuts

The candidates who are going to appear in Competitive exams must know the Percentage Formula and Shortcuts, tricks to solve percentage problems. In competitive and many written exams Quantitative Aptitude is the important topic and if the contender knows the percentage formulas and shortcuts then he can solve the topics easily. It is very difficult for the aspirants who don’t know the short tricks to solve percentage problems to complete the paper on time. The examination will be done on given time with the help of all the percentage formulas and shortcuts tricks.

If you want to score good marks then you must keep practicing the important topics daily. Remember the formulas and tricks at the time of examination because it saves your time. Give time to every topic and prepare important subjects from the previous year sample papers. This will boost your confidence and you will be able to solve all the questions speedily. We are providing Some Percentage Formula and Short Ticks that will surely helpful for you.

### Percentage Meaning And Its Examples

Percentage is percent which means parts per hundred (1/100).

If we have to convert percentage into fraction then it is divided by 100.

45% = 45/100 (fractional) or 0.45 (decimal)

Example:

What is 30% of 80?

Solution: x = 30/100 X 80 and we do the math to solve for x. (The answer is 24.)

Example:

Convert decimal into percentage.
If we have to convert fraction into percentage we have to multiple with 100.

0.25 = (0.25 × 100) % = 25%
1.50 = (1.50 × 100) % = 150

Example:

An increase of 30% in the price of oranges enables a man to buy 6 kg less for Rs. 300. Find the increased price per kg.

Solution: The statement implies that the man has 30% of Rs. 300 available to spend on 6 kgs now. 30% of 300 = 30/100 x 300 = 90
So the increased price per kg is 90/6 = Rs. 15 per kg

The above table will help you solve questions very fast and easily. Try to remember these fractions because it will save lot of time in your examination.

Formulas And Short Tricks
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 (1 + R/100) n
2. Population n years ago =P/ (1 + R/100) n

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 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 (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%

Note: For two successive changes of x% and y%, net change = {x + y +xy/100} %

Percentage – Ratio Equivalence:

Converting Fractions, Decimals To Percents:

Percent to Decimal: move the decimal point two places to the left. For example, 42% = 0.42.

Percent to Fraction: place the percent number in the numerator and 100 in the denominator; simplify. For example, 42% = 42/100 = 21/50.

Decimal to Percent: move decimal point two places to the right, For example, 1.6 = 160%.

Fraction to Percent: first convert fraction to decimal, then follow the directions to convert from decimal to percent. For example, 5/6 = 0.833 repeating = 83 and 1/3 %.

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Percent Change Type of Questions

Percent increase or decrease is one way to represent a change in a given number. Percent increase is the percentage that the original number increases and percent decrease is the percentage that the original number decreases.

Simple Formula

Increase (or Decrease) = (Change / Original) * 100

Example- You had your eye on a \$100 Trouser at the store, but you think it’s too expensive. Finally, it goes on sale for \$60. What is the percent decrease?

Answer- There is always the difference between our starting and ending points. In this case, it’s 100 – 60 = 40. The “original” is our starting point; in this case, it’s 100. (40/100)*100 = (0.4)*100 = 40%.
Example- If price of an article is increased by 33.33%, by what % it needs to be decreased to make it to the same price?

Answer- Increased by 33.33% means 1/3 so need to reduce by 1/(3+1)= ¼ =25%.

Point to Remember

If there is 1/x fractional increase then you will have 1/(x+1) fractional decrease and vice versa.

Multiple Percent Change Type of Question

Question- Two years ago, the population of a street in Los Angles was 250. Last year, the population increased by 20% and this year the population is expected to increase another 10% in that street. How many residents is that street of Los Angles expected to have at the end of this year?

Let’s look at the right way and the wrong way to do this problem:

First, the right way: Street of Los Angles starts out with a population of 250. In the first year, the population increases by 20%, so we add 50 people (practice Fast Math here: 10% + 10% = 20%, so 25 + 25 = 50). Our new population is 250 + 50 = 300. This year, Los Angles will add 10% but, this time, 10% is based on the new population figure of 300, not the old figure 250. This year, we add 30 people, so our population at the end of the year is expected to be 300 + 30 = 330.

Now, the wrong way: If we just add 20% and 10%, for an increase of 30%, we would have said that our population is based on a 30% increase of the 250 figure, or 75 (10% + 10% + 10% = 25 + 25 + 25 = 75). Our final answer would be 325. You can expect this number to show up in the answer choices, so you would not realize it if you made this mistake.

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Official Note:

We hope that the above information will be helpful for you at the time of examination. Keep practicing the short cut tricks and percentage formulas daily so you can complete the question paper speedily and you can score better marks. At last we wish to say all the best to the aspirants who are going to take exams. Do you well and don’t get confused between similar type of questions.