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PERCENTAGE

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...........................PERCENTAGE...........................


Percentage
The word percent can be understood as follows:Per cent => for every 100.
So, when percentage is calculated for any value, it means that you calculate the value for every 100 of the reference value. When you see the word "percent" or the symbol %, remember it means 1/100.

Why Percentage?
Percentage is a concept evolved so that there can be a uniform platform for comparison of various things. (Since each value is taken to a common platform of 100) 


Example: To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another.
1. 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
2. Commodity Price Increase/Decrease:
A.  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)*100
B. If the price of the commodity decreases by R%, then to maintain the same expenditure by increasing the consumption is:
=  (R /100-R)*100
Percentages – Fractions Conversions:
For faster calculations we can convert the percentages or decimal equivalents into their respective fraction notations. The following is a table showing the conversions of percentages and decimals into fractions:

Percentage

Decimal

Fraction
10%
0.1
1/10
12.5%
0.125
1/8
16.66%
0.1666
1/6
20%
0.2
1/5
25%
0.25
1/4
30%
0.3
3/10
33.33%
0.3333
1/3
40%
0.4
2/5
50%
0.5
1/2
60%
0.6
3/5
62.5%
0.625
5/8
66.66%
0.6666
2/3
70%
0.7
7/10
75%
0.75
3/4
80%
0.8
4/5
83.33%
0.8333
5/6
90%
0.9
9/10
100%
1.0
1

Converting decimals:
We can go for converting decimals more than 1 from the knowledge of the above cited conversions as follows:
We know that 12.5%=0.125=1/8
Important Points to Note:
When any value increases by
10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)
20%, it becomes 1.2 times of itself.
36%, it becomes 1.36 times of itself.
4%, it becomes 1.04 times of itself.
Thus we can see the effects on the values due to various percentage increases.
When any value decreases by
10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)
20%, it becomes 0.8 times of itself
36%, it becomes 0.64 times of itself
4%, it becomes 0.96 times of itself.
Thus we can see the effects on a value due to various percentage decreases.
Note: 1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.
2. The percentage increase or decrease depends on the decimal multiplied.
Example: When the actual value is x, find the value when it is 30% decreased.
Solution: 30% decrease => 0.7 x.
Example: A value after an increase of 20% became 600. What is the value?
Solution: 1.2x = 600 (since 20% increase)=> x = 500.
Example: If 600 is decrease by 20%, what is the new value?
Solution: new value = 0.8 * 600 = 480. (Since 20% decrease)
Thus depending on the decimal we can decide the % change and vice versa.

Example: When a value is increased by 20%, by what percent should it be reduced to get the actual value?
Solution:(It is equivalent to 1.2 reduced to 1 and we can use % decrease formula)
%decrease=(1.2–1
/1.2
)*100=16.66%
When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes.
Example: The population of a town increased by 10%, 20% and then decreased by 30%. The
new population is what % of the original?
Solution: The overall effect = 1.1 * 1.2 * 0.7 (Since 10%, 20% increase and 30% decrease)
= 0.924 = 92.4%.
Example: Two successive discounts of 10% and 20% are equal to a single discount of ___
Solution: Discount is same as decrease of price.
So, decrease = 0.9 * 0.8 = 0.72 => 28% decrease (Since only 72% is remaining)


1. 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:
39, 30
41, 32
42, 33
43, 34
2  .A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
588 apples
600 apples
672 apples
700 apples
3.   If A = x% of y and B = y% of x, then which of the following is true?

A is smaller than B.
A is greater than B
Relationship between A and B cannot be determined.
If x is smaller than y, then A is greater than B.
None of these
4.  A student multiplied a number by
3
instead of
5
.
5
3
    What is the percentage error in the calculation?
34%
44%
54%
64%
5. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
2700
2900
3000
3100
6. In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500. The marks obtained by A were (A). 405                                     (B). 450
(C). 360                                      (D). 400

7.) Find the single discount equivalent to a series discount of 20%, 10% and 5%

A. 42.60 %                         B. 57.18%

C. 68.40%                          D. None of these

8. If number x is 10% less than another number y and y is 10% more than 125, then x is equal to




9. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are





10. 270 students appeared for an examination, of which 252 passed. The pass percentage is





11. Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss or gained

a.25%
b. 50%

C.  75%


12.  88% of 370 + 24% of 210 - x = 118
  A.150                                B.250
  C.158                               D.258
13. Evaluate 28% of 450 + 45% of 280
A.     232                             B.   242
C.     252                             D.    262
14.  If 15% of 40 is greater than 25% of a number by 2, the number is                    
 A.14        B.16              C.18     D.20
15. Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen.
A.Rs. 9.36            B.Rs. 10.36
C. Rs. 11.36         D.Rs. 12.36
16. In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.
A.40%                B.42%
C.44%                D.46%
17.In an acoustics class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students. 20% of the male engineering students and 25% of the female engineering students passed the final exam. What percentage of engineering students passed the exam?
A. 5%                              B. 10%
C.16%                             D. 22%
18.If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
A. 25%                          B. 16.67%
C. 20%                          D. 33.33%
19.A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

A.
50
B.
100
C.
150

D.
200


20.The an examination 80 % candidates passed in English and 85% in Mathematics. If 73% candidates passed in both subjects then how many candidates were failed in the both subjects?
A) 8               B) 15                 C) 27                   D) 35

21.There is 20% decrease in cost of sugar. Now a person can get 500 gm of sugar more in Rs. 36. What was the original cost of sugar per kg?
A) Rs. 14.40                         B) Rs. 18
C) Rs. 15.60                         D) Rs. 16.50

22.If the length of a rectangular field is increased by 5% and breadth decreased by 10%, then what will be the difference in its area ?
A) 5.5% increase                               B) 5.5% decrease
C) 0.55% decrease                           D) No change

23.  B got 20% less marks than A. Then A got how many percentage more marks than B?
A) 20B) 25
C) 12D) 80

24.The population of a village is increased by 4%. If present population is 50,000 then what will be it after 2 years?
A) 53,900                                   B) 54,000
C) 54,080                                  D) 54,900

25.If x earns 25% more than y. What percent less does y earn than x?
A) 16                                       B) 10
C) 20                                        D) 25



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