Aptitude ➤ Percentage ➤ Set 1

#### Percentage : Important Facts and Formulae

1. Concept of Percentage: 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 .
To express a/b as a percent: We have, a/b = (a/b) x 100 %.
Thus, 1/4 = (1/4) x 100 % = 25 %.

2. Percentage Increase/Decrease:

If the price of a commodity increases by R %, then the reduction in consumption so as not to increase the expenditure is:

[R/(100 + R)] x 100 %

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

[R/(100 - R)] x 100 %

3. Results on Population:
Let the population of a 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

4. Results on Depreciation:
Let the present value of a machine be P. Suppose it depreciates at the rate of 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
3. If A is R % more than B, then B is less than A by [R/(100 + R)] x 100 %.
4. If A is R % less than B, then B is more than A by [R/(100 - R)] x 100 %.
Question 1
Q1.  An inspector rejects 0.08% of the meters as defective. How many will be examine to reject 2 ?
Question 2
Q2.  Rent of a coffee shop is increased from Rs. 4000 to Rs. 4400. Find the increase in price as a percentage of the original rent.
Question 3
Q3.  A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had :
Question 4
Q4.  A positive number is divided by 5 instead of being multiplied by 5. By what percent is the result of the required correct value ?
Question 5
Q5.  A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets ?