This document provides information on percentages and percentage calculations. It includes sections on the relationship between percentages and fractions, percentage change calculations, successive increases and decreases, product constancy, and partnerships. Examples of percentage problems are provided throughout with step-by-step explanations. The document is intended as a study guide for bank exams and other competitive exams that include questions on percentages.

1. Bank Exams and SSC
Percentages – Concept Session
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2. www.georgeprep.com
Topics Break-up
Percentage –Fraction Relationship
Percentage Change calculations
Successive Increases/decreases
Product Constancy
Partnerships
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3. • Percentage –Fraction Relationship
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4. Percentage – What does it mean?
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Of the total 300 students, only 150 have appeared for the exam.
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5. Percentage & Fraction
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 Only 3/4th of the participants who registered for the
event have turned up.
Fraction to Percentage
Percentage to Fraction
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6. Percentages, fractions decimals and ratios
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 50% of the students appeared for the exam
Fraction
Decimal
Ratio
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7. Percentages, fractions decimals and ratios
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Fraction
Percentage
Equivalent
1/1 100
½ 50
1/3 33.33
¼ 25
1/5 20
1/6 16.67
1/7 14.28
1/8 12.5
1/9 11.11
1/10 10
Fraction
Percentage
Equivalent
1/11 9.09
1/12 8.33
1/13 7.69
1/14 7.14
1/15 6.66
1/16 6.25
1/17 5.88
1/18 5.55
1/19 5.26
1/20 5
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8. • Percentage-Change calculations
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PERCENTAGES
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9. Percentage change calculations
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Percentage change =
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒
𝑥 100
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10. Percentage change calculations
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100
230
0
50
100
150
200
250
2003 2014
InINR
Price of a movie ticketWhat is the percentage change
in the price of a movie ticket
from 2003 to 2014?
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11. Percentage change calculations – Significant fraction
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100
230
0
50
100
150
200
250
2003 2014
InINR
Price of a movie ticketSignificant Fraction
Percentage change =
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒
x 100
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12. Percentage change calculations – Of and than
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A is what percentage of B?
A is what percentage more than B?
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𝐴
𝐵
× 100
𝐴 − 𝐵
𝐵
× 100
A is what percentage less than B?
𝐵 − 𝐴
𝐵
× 100

13. Percentage change Vs. Percentage Point change
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30%
33%
28%
29%
30%
31%
32%
33%
34%
2000 2012
Tax rate
Percentage Change in Tax rate
Percentage point change in
Tax rate
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14. Percentage change representation
 As fractions  As decimals
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(1 ± 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡) (1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡)

15. Problems
If John’s salary were 20% higher, it would be 20% less than
Smith’s. If Smith’s salary is Rs.90,000, what is John’s salary?
(A) Rs.36,000
(B) Rs.40,000
(C) Rs.60,500
(D) Rs.42,850
(E) Rs.65,000
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Answer: option E

16. Successive Increases-Decreases- Problems
Bhavna decided to donate 12% of her salary to an orphanage. On the
day of donation she changed her mind and donated Rs.2,400/ which
was 125% of what she had decided earlier. How much is Bhavna's
salary?
A) Cannot be determined
B) Other than those given as options
C) Rs.14,750/-
D) Rs.18,500/-
E) Rs.16,000/-
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IBPS PO Main
(2015)
Answer: option E

17. Successive Increases-Decreases- Problems
In an election between two candidates, one got 52% of total valid
votes. 25% of the total votes were invalid. The total number of votes
were 8400. How many valid votes did the other person get?
(1) 3276
(2) 3196
(3) 3024
(4) Cannot be determined
(5) None of these
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Bank of Maharashtra PO
(2008)
Answer: option 3

18. Percentages
• Successive Increases/decreases
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19. Successive increases/decreases
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Formula Method:
𝑥 + 𝑦 +
𝑥𝑦
100
(𝐹𝑜𝑟 𝑡𝑤𝑜 𝑠𝑡𝑒𝑝𝑠)
𝑥 + 𝑦 + 𝑧 +
𝑥𝑦 + 𝑦𝑧 + 𝑥𝑧
100
+
𝑥𝑦𝑧
1002 (𝐹𝑜𝑟 𝑡ℎ𝑟𝑒𝑒 𝑠𝑡𝑒𝑝𝑠)
Decimal Method:
1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞. × 1 ± 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑒𝑞. … − 1 × 100

20. Successive increases/decreases
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Increase and decrease by x%
𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑜𝑓
𝑥2
100
%

21. Successive increases/decreases – Order matters?
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22. Successive Increases-Decreases- Problems
A number is decreased by 10% and the resulting number is
again decreased by 20%, what is the final percentage of
decrease?
1) 25%
2) 26%
3) 27%
4) 28%
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SSC CGL Tier-I
(2016)
Answer: option 4

23. Successive Increases-Decreases- Problems
The strength of a school increases and decreases in every
alternate year by 10%. It started with increase in 2000. Then,
the strength of the school in 2003 as compared to that in 2000
was
1) increased by 8.9%
2) decreased by 8.9%
3) increased by 9.8%
4) decreased by 9.8%
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23
SSC CGL Tier-II
(2014)
Answer: option 1

24. Successive Increases-Decreases- Problems
Mr Shamin’s salary increases every year by 10% in June. If
there is no other increase or reduction in the salary and his
salary in June 2011 was ₹ 22,385, what was his salary in June
2009?
1) ₹ 18,650
2) ₹ 18,000
3) ₹ 19,250
4) ₹ 18,500
5) None of these
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SBI PO
(2011)
Answer: option 4

25. Successive Increases-Decreases- Problems
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 the percentage of students who passed in both the
subjects was :
A) 40 %
B) 42 %
C) 44 %
D) 46 %
E) 48 %
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SBI Clerks Main
(2016)
Answer: option C

26. Percentages
• Product Constancy
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27. Product constancy
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28. Product constancy
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1. The length of a rectangle is increased by 50%, what
should be the percentage decrease in the breadth to keep
the area constant?
2. The length of a rectangle is decreased by 50%, what
should be the percentage increase in the breadth to keep
the area constant?
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Answers:
1. 33.33%
2. 100%

29. Product constancy line
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𝟏
𝟏
𝟏
𝟐
𝟏
𝟑
𝟏
𝟒
𝟏
𝟓
𝟏
𝟔
𝟏
𝟕
𝟏
𝟖
𝟏
𝟗
𝟏
𝟏𝟎
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30. Product constancy
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Increases followed by decreases
Decreases followed by Increases
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31. Product constancy
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The length of a rectangle is increased by 50%, what should
be the percentage decrease in the breadth to keep the
percentage increase in area at 20%?
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Answer: 20%

32. Product Constancy - Problems
The product of one-third of a number and 150% of another
number is what per cent of the product of the original
numbers?
1) 80%
2) 50%
3) 75%
4) 120%
5) None of these
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SBI PO
(2011)
Answer: option 2

33. Percentages
• Partnerships
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34. Partnerships- Problems
A & B start a business. B invests an amount which is Rs
500 more than A. At the end of six months from the start of
business, A and B double their respective investments. If
the annual profit earned was Rs. 5200 and A’s share from
the annual profit was Rs. 1600, what was A’s initial
investment ?
A) 1000
B) 800
C) 750
D) 400
E) 800
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34
IBPS Clerks Prelims
(2016)
Answer: option D

35. Partnerships- Problems
Pihu and Rani start a business together by investing Rs.
9000 and Rs. 6300 respectively. After a certain period,
Pihu withdrew from the business completely. If at the end
of 2 years the total profit earned was Rs 13500 and Pihu’s
share was Rs. 6750 , after how many months did Pihu
withdraw from business ?
A) 23 months
B) 14 months
C) 20 months
D) 18 months
E) 15 months
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35
SBI Clerks Prelims
(2016)
Answer: option D