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__Percentage Important Aptitude Formulas__:

__Percentage Important Aptitude Formulas__:

**(I). Concept of Percentage:**

1. 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.**
Thus, 20% =20/100 =1/5;

48% =48/100 =12/25, etc.

2.
Percentage increase = (increase/original) × 100

3.
Percentage decrease = (decrease/original) × 100

4. Increased
value at rate of x% after time‘t’ be

Increased value = Present
value × [(100 + x)/100]

^{t}
Decreased value = Present
value × [(100 - x)/100]

^{t}
5. Initial
value that is increased to present value at the rate of x% in time t, then

Initial value = present value ×
[100/(100 + x)]

^{t}
6. Initial
value that is decreased to present value at the rate of x% in time t, then

Initial value = present value ×
[100/(100 - x)]

^{t}**(II) Results on Population:**

Let the
population of the town be P now and suppose it increases at the rate of R% per
annum, then:

1. Population after n years = P × [1 + (R/100)]

^{n}
2. Population n years ago = P/[1 + (R/100)]

^{n}**(III). Results on Depreciation:**

Let the
present value of a machine be P. Suppose it depreciates at the rate R% per
annum. Then,

1. Value of the machine after n years = P
× [1 - (R/100)]

^{n}
2. Value of the machine n years ago = P/[1
- (R/100)]

^{n}**(IV).**If A is R% more than B, then B is less than A by [(R/(100 + R)) × 100]%.

If A is R% less than B, then B is more
than A by [(R/(100 - R)) × 100]%.

__Example: 01__**If the sales tax reduced from 3**

**½ % to 3⅓ %, then what difference does it make to a person who purchases an article with market price of Rs. 8400?**

__Solution:__**Required difference = [3½ % of Rs.8400] – [3⅓ % of Rs.8400]**

= [(7/2) - (10/3)]
% of Rs.8400 =1/6 % of Rs.8400

= Rs. [(1/6)
× 8400] × (1/100) = Rs. 14.

__Example: 02__**A man calculates that if he lets his house for Rs 80 per month, he would earn 7½ % p.a on his outlay after allowing for repairs. Actually he is able to let it for Rs. 76 p.m and had to spend Rs. 60 more on repairs. He thus gets only 6% p.a on his outlay. Find the outlay?**

**Let, price of the outlay is**

__Solution:__*x*.

Therefore, 1½ % of

or, (3/2) × (

or, *x*= (4 × 12) + 60or, (3/2) × (

*x*/100) = 108*x*= 7200

**Percentage Aptitude:**

**Formula: Percentage Aptitude Formulas**

**Solved Examples: Solved Examples: Set 01**

**Practice Test: Practice Test: 01 Practice Test: 02**

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