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Basics of Percentages Study Notes for SSC CGL & CPO 2017

Percentage is an important part of Quantitative aptitude. Whether it is DI, Profit & Loss, SI-CI, or Allegation, etc. all these chapters with the help of percentage can be solved easily. You can go through the basics of percentage and previous year asked questions. 

A percentage is a number or ratio expressed as a fraction of 100.It is a proportion per hundred. 
  1. When we say 35 percent in mathematical notation we write 35%. 
  2. When we want to express this in mathematical form, 35% means 35 per 100 or (35/100).

Important: 50% of 20 can be written 20% of 50 as well.
You can also represent % into decimal, 50% = 0.5
Conversion of fraction into %.

to convert fraction into %, we multiply it by 100.
¼ = (¼)× 100 % = 25 %.
1/3 = (1/3) ×100 % = 33(1/3) %
1/14 = (1/14) ×100 % = (100/14)%=(50/7)%= 7 (1/7) %
Note: Never forget to express % notation in the percentage. 




We suggest you that you must learn both tables given below.


Fraction

Percentage

Fraction

Percentage

Fraction

Percentage

1 100% 1/7 14(2/7) % 1/13 7 (9/13) %
1/2 50% 1/8 12(1/2) % 1/14 7 (1/7) %
1/3 33(1/3) % 1/9 11(1/9) % 1/15 6 (2/3) %
1/4 25% 1/10 10 % 1/16 6 (1/4) %
1/5 20% 1/11 9 (1/11) %
1/6 16(2/3) % 1/12 8 (1/3) %


Conversion of % into fraction.

To convert % into fraction, we divide it by 100. So, we can express in this way:
100% = (100/100) = 1        1% = (1/100)    2% = (2/100) = (1/50)
50% = 50/100 = ½
20% = 20/100 = 1/5
10% = 10/100 = 1/10
16(2/3)% = (50/3)% =50/(3×100) = 50/300 = 1/6

Percentage

Fraction

Percentage

Fraction

Percentage

Fraction

10% 1/10 16 (2/3)% 1/6 15% 3/20
20% 1/5 66 (2/3) % 2/3 7(1/2)% 3/40
40% 2/5 6(1/4)% 1/16 22(1/2)% 9/40
60% 3/5 18(3/4) % 3/16 69(3/13) % 9/13
80% 4/5


In following examples we will try to avoid calculation using above table.(i) 99% of 840
we can say 10% = 84,So 1% = 8.4
99% of 840 = 840-8.4=831.6
(ii)25% of 320 = (1/4)× 320
                       =80
(iii) 76% of 400?
      76%=50%+25%+1%
             = 200+100+4
             = 304
(iv) 102% of 720?
       1%= 7.2 so 2%= 14.4
       102% = 100%+2%= 720+14.4 = 734.4
(v)18% of 300?
     18% = 20%-2%= (1/5)×300-6
             = 60-6 = 54
 or 1% = 3 so 18%= 18×3=54
(vi)  12% of 540?
       1%=5.4
       12% = 10%+2+
               = 54+10.8
               = 64.8



    







Example1: Out of his total income, Mr. Sharma spends 20% on house rent and 70% of the rest on house hold expenses. If he saves Rs 1,800 what is his total income (in rupees)?
Solution: Let Income of Mr. Sharma is 100
then he spends 20% on house, so remaining amount is 80.
now he spends 70% of 80 on house hold expenses, so remaining amount left with him is 30% of 80
30% of 80 = 1800
 24 = 1800
   1 = 1800/24
   1 = 75
100= 7500
hence total income is 7500 Rs.
Or, Let total income is P
(100%-20%)×(100%-70%)× P = 1800
80%× 30%× P=1800
((80×30)/(100*100)) × P = 1800
P = 7500

Example2: An army lost 10% its men in war, 10% of the remaining due to diseases died and 10% of the rest were disabled. Thus, the strength was reduced to 729000 active men. Find the original strength.
Solution: Let army has 100 men.
10% loss in war, so remained are 90 men
then,10% of 90 died due to diseases, remained 90-9 = 81
then again, 10% of 81 again disabled
So, remained men = 90% of 81
90% of 81 = 729000
(90×81)/100 =729000
1= 10000
100 = 1000000
hence total men are 1000000.

Example3: In a village three people contested for the post of village Sarpanch. Due to their own interest, all the voters voted and no one vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral per cent of votes?
Solution: As given, no vote was invalid i.e. 100% votes were polled and all candidate got votes in integer value. There were 3 candidates, one losing candidate got 30%, so remaining two candidates got 70% vote of the total.
Candidate 1 + candidate 2 = 70%

Important point which is given in question is minimum absolute margin and integral value. Case 1: Suppose candidate 1 got 40%, then candidate 2 had got 30%. But this is not mininmum absolute margin.
Case 2: Both got 35% votes, If both got equal votes then there will be no winning candidate.
Case 3: One candidate must have got 34% and another one have got 36%.
Hence absolute margin is 2%.

Example4: The difference between 4/5 of a number and 45% of the number is 56. What is 65% of the number?
Solution: Let number is P.
we can say 4/5 = 80%
so, (80%-45%) of P = 56
35% of P = 56
 P = (56/35%)
65% of P = 56/35 ×65 = 104
             
Example5: Deeksha’s science test consist of 85 questions from three sections- i.e. A, B and C. 10 questions from section A, 30 questions from section B and 45 question from section C. Although, she answered 70% of section A, 50% of section B and 60% of section C correctly. She did not pass the test because she got less than 60% of the total marks. How many more questions she would have to answer correctly to earn 60% of the marks which is passing grade?
Solution: If she has done 60% of total questions she would have passed,.
So, no. of question to be done to  pass= 60% of 85 = (3/5)×85 = 51
But she done 70% of A = 70% of 10 = 7
                     50% of B = 50% of 30 = 15
                     60% of C = (3/5) of 45 = 27
So , total questions she attempted =  (7+15+27) = 49
If she has attempted (51-49) = 2 more questions she would have passed.

Example6: In an election between 2 candidates, 75% of the voters cast their votes, out of which 2% votes were declared invalid. A candidate got 18522 votes which were 75% of the valid votes. What was the total number of voters enrolled in the election?
Solution: Let total number of voters enrolled are P.
Number of votes casted = 75% of P = (75/100) P = 0.75 P
Important: Those votes which were declared invalid are 2% of casted voted not 2% of total votes.So, valid votes are = (100%-2%) of 0.75P = 98% of 0.75P
Given Candidates got 75% of valid votes = 18522
(75%) × 98% × 0.75 P = 18522
(3/4) * (98/10) * (3/4) P = 18522
P = 42 × 800
P = 33600 votes.

Example7: An ore contains 20% of an alloy that has 85% iron. Other than this, in the remaining 80% of the ore, there is no iron. What is the quantity of ore (in kg) needed to obtain 60 kg of pure iron?
Solution: Let quantity of ore is P kg
P × 20% × 85% = 60kg
P × (1/5) × (17/20) = 60
P = (60×5× 20)/17
P = 6000/17 Kg
   
Example8: 5% of one number (X) is 25% more than another number (Y). If the difference between the numbers is 96 then find the value of X?
Solution : Given: 5% of X = Y + 25% of Y
0.05 X = 1.25 Y
 X = 25 Y
X-Y=96
25Y-Y =96
24Y=96
Y = 4 so, X =100

All the Best for your Exams.
Team AIMSUCCESS...!!      
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