In Mathematics, a percentage is a ratio or fraction with 100 where 100 is taken as denominator and the percentage is denoted with “Percent Sign (%)”. For example, 95% equals 95/100. In ancient Rome, long before the introduction of decimal system, King Augustus levied a tax (known as centesima rerum venalium) at the rate of 1/100 on the value of goods sold at auction. The computation of this tax was very similar to our present day percent computing system.

Percent decreases or increases are the measures of percent changes. The calculation of percent change tells us the extent to which some value has lost or gained. The computation of percent change is very important to understand changes in a value over time.

First we will look at a situation of percent increase:

Percent Increase

Case 1: Anusha works in a bank for $50.00 per hour. If her pay is increased to $60.00, then what is her percent increase in pay?

Analysis: If we want to find out the percent increase, we must know: (a) the amount of her pay increase per hour, (b) Secondly, we have to ascertain her rate of pay increase by dividing the pay increased amount by her earlier pay. Once we have found the rate of her pay increase over the earlier pay, to find out the percentage increase of her pay, (c) we have to simply multiply that rate with 100 with % sign.

Here how we go:

(a)    Amount of her pay increase per hour = $60 — $50 = $10

(b)   Rate of pay increase = $10 divided by $50 or, $10 / $50 = .

(c)      Percentage increase of her pay = (⅕ × 100) % = 20%

Now, we will learn how percent decrease is calculated.

Percent Decrease

Case 2: Now let’s assume, her salary decreased to $35 per hour from present $50 per hour. If we are to compute the percentage decrease in her salary from present earning per hour, the computation will involve similar calculation except instead of working out the amount of her pay increase per hour, we have to first find out: (a) amount of her pay decrease per hour, (b) In the second step again, instead of working out the rate of her pay increase as we have done earlier, we will find out her rate of pay decrease, by dividing the pay decreased amount by her earlier pay and (c) At the last step, like before, we will multiply the rate of pay decrease as per the previous step (b) with 100%.

(a)    Amount of her pay decrease = $50- $ 35 = $15

(b)   Rate of pay decrease = $15 divided by $50 or, $15 / $50 = 3 / 10

(c)      Percentage decrease of her pay = (3/10 × 100) % =30%

So, to calculate percent change, the following formula is used.

Thus, in simple words to conclude, percent change simply involves,

(i)             Finding the difference between the two numbers (new and old) through subtraction

(ii)            Writing the above result as a fraction.

(iii)           Multiplying it by 100 (percentage)

There are many other situations also when percentage changes is calculated with different objectives. Suppose, the price of a phone was $500. The manufacture decided to offer some discount and marked the new price at $450.

The discount percent offered on the earlier price is,

($500 – $450) / 500 X 100% = 10%.

Now, if any buyer who was unaware of the earlier price but came to know that it is presently being sold at  10% discount and want to deduce the earlier price, simply adds 10% to the present selling price to arrive at the earlier sale price, he will be wrong by adding 10% on $450.  Because, in that case, the price he will calculate will be $450 + $ 45 (i.e., 10% of $450) or $495.

The correct way to find out the earlier price we will be like the following:

The present price is 90% of the earlier price. So $450 is the 90% price of the earlier price.

Therefore, 100% of the earlier price will be ($ 450 / 90) X 100 = $500 [By Unitary Method].