This document provides examples and explanations for percentage problems involving finding a percent of a whole number, finding what percent one number is of another, and finding the whole number when a percent of it is given. It also gives examples of calculating percentage increases and decreases. Several word problems are worked out step-by-step involving marking up prices by a percentage and allowing a discount, increases and decreases in areas and perimeters of shapes when dimensions change by a percentage, and calculating the percentage one number is of another.

1. QA03 PERCENTAGE

2. QUANTITATIVE
PERCENTAGE PROBLEMS
Find a percent of a whole.
Example: What is 15% of 50?
Find what percent one number is of another number.
Example: 10 is what percent of 40?
Find the whole when the percent of it is given as a
part.
Example: 20 is 40% of what number?

3. PERCENTAGE
Find a percent of a whole.
Example: What is 15% of 50?
15 is the %
50 is the “of ”
What is the “ is ”
100
%
of
is
100
15
50
What

4. PERCENTAGE
 Find the whole when the percent of it is given as a part.
Example: 20 is 40% of what number?
40 is the %
what is the “of ”
20 is the “ is ”
100
%
of
is
100
4020
what

5. PERCENTAGE
 Find what percent one number is of another number.
Example: 10 is what percent of 40?
What is the %
40 is the “of ”
10 is the “ is ”
100
%
of
is
10040
10 what

6. Percentage

7. Example – 1
• The Salary of a worker is first increased by
10% and thereafter decreased by 5%.
• What is the overall change in percent.
• overall change = + 10 - 5 + (+10)(-5)/100
• = + 4.5 % (increased)
• use (+) sign for increment and (-) sign for
decrement.

8. Example – 2
• A shopkeeper marks the price of goods 20%
more than the real price. He allowed a
discount of 10%.What profit or loss did he
get?
• Profit or loss the shopkeeper get:
• 20 - 10 + (+20)(-10)/100 = + 8% (profit)

9. Example 3
• The side of a square is increased by 30%. Find
the percentage increase in area.
• Increase in area = 30 + 30 + (30)(30)/100 =
69%.

10. Example 4
• If the radius of a circle is decreased by 20%.
What percent change in area?
• percent change in area:
• - 20 - 20 + (-20)(-20)/100 = -36% (decreased)

11. Example 5
• If the price of a shirt is increased by 15% than
decreased by 15%. What is percent change?
• percent change :
• + 15 - 15 + (+15)(-15)/100 = - 2.25 %
(decreased)

12. Example 6
• The length of a rectangle is increased by 40%
and breadth is decreased by 40%. Find change
in area.
• percent change in area:
• 40 - 40 + (-40)(+40)/100 = -16%(decreased)

13. Example 7
• if a number is increased by 20% and again
increased by 20%. By what percent should the
number increased.
• percent increased:
• 20 + 20 + (+20)(+20)/100 = 44%(increased)

14. Percentage – 2

15. Example 1

16. Example 2

17. Example 3

18. Percentage – 3

19. Example 1

20. Example 2

21. Percentage – 4

22. Example

23. Percentage – 5

24. Example 1

25. Example 2

26. Percentage – 6

27. Percentage – 7

28. Example 2

29. Percentage Increase / Decrease

30. percentage
when subtracted then add
this%
when added then subtarct
this%
4 4.16 = 1/24 3.86 = 1/26
5 5.26 = 1/19 4.76 = 1/21
10 11.11 = 1/9 9.09 = 1/11
12.5 14.28 = 1/7 11.11
15 17.55 13
20 25 16.67 = 1/6
25 33.33 20 = 1/5
30 42.8 23
40 66.67 = 2/3 28
50 100 33.33 = 1/3
60 150 37.5 = 3/8
Example – If the price of sugar increases then by how much % should one
reduce his consumption to avoid extra expenditure.
When price of sugar is increased by 50% the consumption will reduce by
33.33%and like wise.

31. Results on Population

32. Results on Depreciation

34. 1. 60% of 264 is the same as:
a)10% of 44 b)15% of 1056 c)30%of 132 d)none.
• 60% of 264 is more than 132.
• Hence choice a and c is not possible.
• 50% of 264 + 10% of 264
• 132 + 26.40 = 158.4
• 10% of 1056 + 5% of 1056
• 105.6 + 52.8 = 158.4

35. 2. What percent of Rs.2650 is Rs.1987.50?
a)60% b)75% c) 80% d) 90%.
b. %.75%100
100
1
265
19875
%100
2650
50.1987