### Percentage- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems related percentage. Percentage is among most important topic as a lot of questions from DI (Data Interpretation) and Numerical Ability are based on percentage calculations and without knowledge of shortcut tricks and good practice you can waste a lot of time. So candidates are required to prepare this section on preference basis to get success in various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams and placement papers.

### What is percentage (%):Percentage means parts per hundred or a fraction whose denominator is always hundred.

Like if there are 10 red balls in a pack of 100 balls, so percent of red balls is 10%.

Or

If total population of a small village is 100 with 52% women, so we can conclude that there are 52 women in the village.

For calculation purpose we always express percentage as a fraction with denominator as 100.

Like A% = A/100, or 70% = 70/100;  5% = 5/100.

### Case 1: A% of B = B * (A/100)

Eg 1: 25% of 500 = 500 * (25/100) = 125

Eg 2: If a candidate scored 67% marks out of maximum 700 marks. Find the marks scored by the candidates?
Soln: Here we have to find 67% of 700 = 700 * (67/100) = 469

### Case 2 (I): A is what percent of B = (A/B) * 100

Approach / Derivation:
Let A is x% of B
We can write it as A =  (x/100) * B
=> x = (A/B) * 100

Eg 1: 3 is what percent of 60?
Soln: Here A = 3; B = 60.
Applying above formula: (3/60) * 100 = 5%
Hence 3 is 5% of 60.

Eg 2: A candidate scored 469 marks out of maximum 700 marks. Find the percentage of marks scored?
Soln: We have to find 469 is what percentage of 700.
= (469/700) * 100 = 67%.
Hence candidate scored 67% marks.

### Case 2 (II): What percentage of A is B = (B/A) * 100 { We are asking Case 2 (I) in reverse order }

Approach / Derivation:
Let x% of A is B
We can write is as (x/100) * A = B
=> x = (B/A) * 100

Eg 1: What percentage of 60 is 3?
Soln: Here A = 60; B = 3;
Applying above formula:  (3/60) * 100 = 5%
Hence 5% of 60 is 3.

Eg 2: A candidate scored 469 marks out of maximum 700 marks. What percentage of 700 is 469?
Soln: Here A = 700; B = 469.
Applying above formula: (469/700) * 100 = 67%.
Hence 67% of 700 is 469.

### Case 3 (I): By what percent is A more than B = {(A-B) / B} * 100

Approach/ Derivative:
To find how much A is more than B, we will subtract B from A = (A - B)
Now we need to find  (A-B) is what percent of B
From Case 2 (I): (A-B) is {(A-B) / B} * 100 % of B
Hence A is more than B by {(A-B) / B} * 100 %

Eg 1: By what percent is 10 more than 5?
Soln: Here A = 10; B = 5;
Applying above formula:  {(10-5)/5} * 100 = 100%.
Hence 10 is 100% more than 5.

Eg 2: Shubham got 350 marks and Vasu got 280 marks in an examination. By what percent is marks of Shubham more than Vasu?
Soln: Here A = 350; B = 280
Applying above formula: {(350-280)/280} * 100 = 25%.
Hence marks of Shbham is 25% more than Vasu.

### Case 3 (II): By what percent is A less than B = {(B-A)/B} * 100

Approach/ Derivative:
To find how much A is less than B, we will subtract A from B = (B - A)
Now we need to find  (B-A) is what percent of B
From Case 2 (I): (B-A) is {(B-A) / B} * 100 % of B
Hence A is less than B by {(B-A) / B} * 100 %

Eg 1: By what percent is 5 less than 10?
Soln: Here A = 5; B = 10;
Applying above formula: {(10-5)/10} * 100 =  50%
Hence 5 is 50% less than 10.

Eg 2: Shubham got 350 marks and Vasu got 280 marks in an examination. By what percent is marks of Vasu less than Shubham?
Soln: Here A = 280; B = 350;
Applying above formula: {(350-280)/350} * 100 = 20%.
Hence Vasu's marks are 20% less than Shubham.

### Case 4 (I): If A is X% more than B than B is less than A by {X/(100+X)} * 100 %

Eg 1: If 10 is 100% more than 5 than 5 is less than 10 by what percentage?
Soln: Here A = 10, B = 5, X = 100;
Applying above formula: {100/(100+100)}*100 = 50%.
Hence If 10 is 100% more than 5 than 5 is less than 10 by 50%.

### Case 4 (II): If A is X% less than B than B is more than A by {X/(100-X)} * 100 %

Eg 1: If Vasu's marks are 20% less than Shubhm, than Shubham's marks are more than Vasu by what percent?
Soln: Here R = 20;
Applying above formula:  {20/(100-20)} * 100 = 25%.
Hence Shubham's marks are 25% more than Vasu.

### Important trick: While finding percentage of anonymous entity, We can assume that entity equal to 100 to ease our calculations.

Eg1: Roshan's salary was decreased by 40% and subsequently increased by 50%. How much does he lose or gain?
Soln: Let us assume Roshan's original salary = Rs. 100.
After Roshan's salary was decreased by 40% = 100 * (40/100) =  Rs. 40.
Now Roshan's salary is 100 - 40 = Rs.60.
Now his salary is increased by 50%. = 60* (50/100) = Rs. 30
Now Roshan's salary becomes 60 + 30 = 90.
We can see that there is decrease of 10% from original salary.

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