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Percentage

Percentage

For all Competitive exams like IAS, PCS, SSC, Bank, Railway, NTPC, SI, Constable CDS, etc. with short tricks

Concept of Percentage and Technique Based on Problems

Percent can be translated as per 100 or out of 100. Percentage is a dimensionless number that is used to indicate the number of parts per hundred that are being considered. The percent sign (%) percent, is frequently used to represent it. For percentage calculations, 100 is used as the starting point.

Let’s suppose that, in a school of 80 students passed out of 100 students in the exam then the passing percentage of students who passed in the exam is 80%.

If the number of students is increased to 200, the percentage will drop to 40%. This is due to the fact that just 40 students out of every 100 passed the exam.

It can be computed mathematically as (80/200)*100=40 percent.

On the other hand, if 40 percent of 200 students passed the exam, the total number of students who passed the exam is 80.

It can be computed mathematically as (40/100)*200=80.

Generally, we have to face three types of problems regarding calculating of percentage(%).

So, we take three variables and formulate for easily calculation;

X% of Y = Z

Case-I If Y and Z are given and X is missing

Then, X =(Z/Y) *100

Example X% of 500 = 300

Then X = 300/500*100 = 60.

Hence, we can say that 60% of 500 is 3000.

Case-II If X and Z are given and Y is missing

Then, Y = (Z/X) *100

Example 60% of Y = 300

Then Y = 300/60*100 = 500.

Hence, we can say that 300 is 60% of 500.

Case-III If X and Y are given and Z is missing

Then, Z = (X*Y)/100

Example 60% of 500 = Z

Then Z = 60*500/100 = 300.

Hence, we can say that 60% of 500 is 300.

Now we discuss problems based on percentage for competitive exams

Convert x% into decimal =  x/100

7% = 7/100 = 0.07 ;    12% = 12/100 = 0.12

Convert fraction into percent

Fraction X/Y =  (X/Y*100)%

 Some Fast Trick for solving questions of examinations

Technique 1. If X% of A is equal to Y% of B then Z% of A = (Y*Z/X) % of B.

Ex: If 20% of A is equal to 12% of B then 15% of A is equal to what percent of B?

Sol. Percent of B = (12*15/20) %

                              = 180/20% = 9%

Technique 2. If there is a percentage rise then the effect of its change can be nullified by 100*x/(100 + x) %

Ex: If the cost of a shirt went up by 20% by what percentage should the cost be reduced to make the price even? 

Percentage reduction required= (100 × 20)/(100 + 20) = 2000/120 = 16.67%

Successive Percentage Change

Technique 3. If a value X increases by a%, b%, c% and so on upto n%, the total rise in % is given by the formula,

Final output = X(1 + a/100)(1 + b/100)(1 + c/100)……….(1 + n/100)

Technique 4. If a value X decreases by a%, b%, c% and so on upto n%, the total decline in % is given by the formula,

Final output = X(1 – a/100)(1 – b/100)(1 – c/100)……….(1 – n/100)

Technique 5. (a) If A is X% more than Y, then Y is (X/100+X * 100) % less than X.
                            (b) If A is X% less than Y, then Y is (X/100-X * 100) % more than X.

Ex. If income of Ram is 10% more than that of Shyam, then income of Shyam is how much per cent less than of Ram?

Required percentage = (10/100+10 * 100)%

                                           =(10/110 * 100)%

                                              = 9.09%

Ex. If income of Ram is 10% less than that of Shyam, then income of Shyam is how much per cent more than of Ram?

Required percentage = (10/100-10 * 100)%

                                           =(10/90 * 100)%

                                               = 11.11%

Technique 6. If the value of a number is first increased by X% and later decreased by X% then the net effect is always a decrease which is equal to X%  of X and is written as X2/100 %.

Ex.  The salary of Ram is first increased by 10% and then it is Decreased by 10%. What is the change in his salary?

Sol. Required change = 102 /100 %

                                             =  100/100% = 1%

Technique 6. If a number X is increased by Y%, then the new number will be   

                           100+Y/100 * X

Technique 6. If a number X is deceased by Y%, then the new number will be           

                            100-Y/100 * X

Technique 7. If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then

Example: – Pankaj Sharma has to score 40% marks to get through. If he gets 40 marks and fails by 40, then find the total marks set for the examination?

Technique 8. If a candidate scores X% marks and fails by a marks while an another candidate scores y% marks and gets b marks more than minimum passing marks, then

Example:- A candidate score 25% and fails by 60 marks, while another candidate who score 50% marks, gets 40 marks more than the minimum required marks to pass the examination. find the maximum marks for the examination.

Sol:  Maximum marks = (60 + 40)/50-25 *100

                                          = 100/25 *100

                                         = 4*100 = 400

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