Preparation of Percentage Problems (%) for Competitive Exams

Percentage in Competitive exams
Percentage
Percentage problems are very easy solvable in Competitive exams. In Competitive exams definitely, 2% of questions will come in this particular area.
We are using the percentages in our daily life. How are we using percentages in our daily life?
 Two business partners had set up a company turnover Rs. 1/- Cr. They had profits for the year Rs. 75 /- lakhs. How had the business partners shared the money?  An amount of Rs. 75 /- Lakhs had been shared as 50% and 50%, that means each business person got Rs. 37.5 lakh .

How can percentage problems helpful in Competitive exams?


These following are the simple basics:

x% mean x hundredths, written as x%
To express x%  as fraction that is x% = x/100
To express a/b as a percentage, we can write as a/b = (a/b x 100)%.

The following are the most frequently asked model questions?

  1. How to calculate percentages? 
  2. How to calculate double percentages? 
  3. If X is subtracted from X% of a number, the result is X again. What is the number? 
  4. If X is added to X% of a number. The result is the number again. What is the number? 
  5. If a number is increased by X%. It becomes Y. What is the number? 
  6. If a number is reduced by X%. It becomes Y and the same number is increased by Z%. What is the number? 
  7. If a  number is increased by X% and decreased by X%. What is the effect? 
  8. If a  number is decreased by X% and increased by X%. What is the effect? 
  9. If a number is decreased by X% and again decreased by X%. What is the effect? 
  10. If A's salary is X% more than that of B, then what percent B's salary less than that of A? 
  11. In an examination X% of students fail in English and Y% pass in Hindi and Z% fail in both. Find the actual failure percentage? 

Here are the frequently asked questions models are given below:


Before going to learn the questions and answer, we need to learn basics things about the percentage. If we do not remember basic percentage results really we need to do hard work to get the answer for the simple problems.  Once we learn thoroughly, there will be no time waste for doing problems in competitive examinations.

Shortcut Methods:
1) 15% of 400 =?
Multiply both the numbers and put a decimal point after two digits from the right side in the final result.
15 * 400 = 60.00 = 60.
The Answer is 60

2) 15% of ? = 60
Answer : Add two zeros to 60 and divide by 15
= 6000/15 = 400

3) ?% of 400 = 60
Answer: Add two zeros to 60 and divide by 400
=6000 / 400 = 15.

Some more answers can quickly be identified when percentages have been given below:


75% =3/4            10%=1/10       33 1% = 1/3      12 1 % = 1/8
50%=1/2             20%=1/5           3                2
25%=1/4             40%=2/5        66 2 % = 2/3     37 1 % = 3/8
12 1%=1/8           60%=3/5           3                2
   2                80%=4/5        16 2 % = 1/6     62 1 % = 5/8
6 1 % = 1/16                          3                2
  4                                 8 1 % = 1/12    87 1 % = 7/8
                                      3                2
                                   11 1 % = 1/9
                                      9
                                    9 1% = 1/11
                                      11

Some more Percentages:


100% = 1 time of the given percentage number.
125% = 1 1/4  times of the given percentage number.
150% = 1 1/2 times of the same percentage number.
175% = 1 3/4 times of the given percentage number.

When comes to the 100 number, there are 100 having

two 50's, four 25's, five 20's, ten 10's, three 33 1/3's, six 16 2/3's, twelve 8 1/3's, eight 12 1/2's, sixteen 6 1/2's, nine 11 1/9's, eleven 9 1/11's.

Questions and Answers:


1. How to find a double percentage of a Number?

  15% of 20% of 300=?
Answer: Normal method:
20% of 300=60
15% of 60=9

Shortcut method:
15 * 20 * 300 = 90000
(NOTE: Put a digit before four digits from the right side)
i.e. =9.0000
=9


2. How to find the missing number in double percentages problem?


I. 15% 0f 20% of ? = 9
Answer: 90000 / 15 * 20
      =300
II. 15% of ?% of 300=9
Answer: 90000 / 15 * 300 = 20

III/ ?% of 20% of 300=9
Answer:  90000 / 20 * 300  = 15

3. Exam based problems;

I. 56% of 43 + 12.78 = ?
Answer: 56 * 43 = 2408  (Put a point before two digits from the right side)
                      = 24.08
Finally = 24.08 + 12.78
             = 36.86
II. 56% of 67 + 48% of 53 =? 
Answer:  56 * 67 = 3752
                       = 37.52
         48 * 53 = 2444
                       = 24.44
  Finally  = 37.52 + 24.44
               = 61.96
III. 57% of 69 + 3/5 of 575 =? 
Answer: 57 * 69 = 3933
                     = 39.33
         3/5 of 575 = 345
Finally = 39.33 + 345

4. If 40 is subtracted from 40% of a number the result is 40 again. What is the number?

Answer: 40 - 40% of x = 40
        if 40%  = 80
           100%  = ?
That means 100 * 80  = 200
                     40


5. The difference between 20% of a number and 1/6 of the same number is 10. What is the number?

Answer: 20% * ? - 1/6 * ? = 10
        ? (20% - 1/6) = 10
        ? (1/5 - 1/6) = 10
        ? (1/30) = 10
        ? = 300    


6. If a number is increased by 25%, it becomes 85. What is the number?

Answer: 100% + 25% = 125%
        If  125% = 85
             100%  = ?
  Therefore 100/125 * 85
                 =  68.


7. If a number is reduced by 25%. It becomes 150. And if the same number is increased by 20%. What is the number?

Answer:
If the number is decreased by 25%
         100% - 25% = 75%
If the same number increased by 20%
           100% + 20% = 120%
  IF 75% = 150  
      120% = ?
 Therefore   120 / 75 * 150 = 240


8. If a number is reduced by 12 1/2%, it becomes 63 and if it is increased by 37 1/2%. What will be the number?

Answer:  If the number is reduced by 12 1/2 %
          100% - 12 1/2% = 87 1/2%
           87 1/2% = 63
 If the number is increased by 37 1/2%
          100% +  37 1/2% = 137 1/2%
If        87 1/2%  = 63
         137 1/2% = ?
Therefore 137.5 / 87.5 * 63 = 99


9. If a number is increased by 10% and decreased by 10%. What is the effect?

Answer: Number increased by 10%
100% + 10%  = 110%
If a number decreased by 10%
110 - 110 (10%) = 99%
1% loss.

NOTE: The square of (X/10) =  100 /100 = 1 % less.

10. If a number is decreased by 10% and again increased by 10%. What is the effect?

Ans: Number is decreased by 10%
 100% - 10% = 90%
 Again is increased by 10%
  90% +90(10%) = 99%
= 1% less.
NOTE: The square of (X / 10) = (10/10)(10 /10) = 1% less.

11. If  A's salary is more than that of B's salary. How much percent B's salary less than that of A'?

Answer:  Formula [R/ (100+R) 100]%
     = [50 / (100+ 50) * 100] %
     = [50 /150 * 100]
     = 33 1/3%
[or]
let's assume    
B's salary = 100%
A's salary = 100% + 50 % = 150%
= 50/150 * 100 = 100/3 = 33 1/3%

12. In the examination, 38% of students fail in English and 61% pass in Hindi and 23% fail in both. Find the actual failure percentage?

Answer:  Fail in English =38%
          Fail in Hindi = 23% (i.e 200 = 23%)
         So fail in Hindi 100% - 61% = 39%
       
Finally 100% => [39 + 38 - 23] =54%

13. The price of the sugar has increased by 60% In order to restore the original price, the new price must be reduced by what percentage?

Answer:
Sugar increased by 60%
= 100% + 60% = 160%
In order  to restore the original price = 60/160 * 100 = 37 1/2%.


14. A's and B's salaries together amount to Rs. 2000. A spends 95% of  his salary and B is 85% of his. If now their savings are the same, what is A's salary?

                     Salary A+B = 2000
Spends:            A = 95%                 B=85%
Savings:         (100-95) = 5%         (100 - 85) =15%          
                   5% x 3 times = 15%      15% x 1 time = 15%
 A:B = 3:1
 A's salary = 3 / 4 * 2000 = Rs. 1500/-
B's salary - 1/4 * 2000 = Rs. 1500/-


15. If the population increases at 4% per annum. What will be the population of a city 2 years hence if it is 81250 now?

Answer:
1st year 81250 * 4/100 = 3250
=81250 + 32500=84500
2nd year 84500 * 4 / 100= 3380
=84500 +3380 = 87880

16.  5 litres of 20% sulphuric acid, 5 litres of 100% pure sulphuric acid is added. What is the strength of the acid in the mixture now?

Answer: 5 litres of 10% = 5 * 20 / 100 = 1%
     5 litres of 100% = 5 100/100 = 5%
Mixture =  1% + 5% = 6%
10 litres of 6% is => 10 * 6/100 = 3/5 = 60%


17. If the sugar is 300% cost of Wheat by what percentage wheat is cheaper than sugar?

Answer: Formulas: Increase = [100+ x/100]100%
                          Decrease = [100-x/100]100%

Wheat    Sugar    Sugar is how much cost of wheat
100%  = 100%  = 100% cost of wheat
100% = 200%   = 200% cost of wheat
100% = 300%   =  300% cost of wheat
How much less -200%
Wheat is 200/300 * 100 = 2/3% =66 2/3 cheaper


18. If sugar is 300% costlier than Wheat, by what percentage Wheat is cheaper than Sugar?

Answer:
Formula  [x / x+ 100] 100%

Wheat    Sugar    Sugar is ?% costlier
100% = 100% = 0%
100% = 200% = 100%
100% = 300% = 200%
100%  = 400% = 300%
The difference is 300%
Wheat is 300/ 400 = 3 /4 = 75%


19. If the price of sugar is increased by 25%, by what percentage the consumption must be reduced in order to maintain the same expenditure?

Answer: Formula= [reduction /100=R] 100
Original Price    increased price    % ? reduced in consumption
100% = 100+ 25 =15

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