Percentage Tricks and formulas - ObjectiveBooks
Percentage Tricks and formulas

Percentage Tricks and 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 3½ % 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?

Solution: Let, price of the outlay is x.
Therefore, 1½ % of x = (4 × 12) + 60
or,     (3/2) × (x/100) = 108
or,     x = 7200
 Percentage Aptitude: Next Tests