Percentages

What will you learn in this lesson on Percentages? Percent means per hundred. (Cent means hundred). Per cent (or percentage) is denoted by the symbol %. The fraction 1/100 is written for percent.

the fraction for percent

Percentage affords clarity and comparison.

Example:

A rebate of $8 on a book costing $40 is 20%, while a rebate of $10 on the same book costing $60 in another shop results in 16.66%. A greater amount of discount is actually a smaller percent of discount. Sometimes, it is just a relative figure.

Example:

John got 20% hike in his salary and Tom, 10% hike. Evidently enough, we cannot conclude John was blessed with a greater amount of hike, unless the actual bases, i.e. the salaries of the two, are available to us. Or, if you wish to capture a terse overview of each Percentages Formula, then go through each of the following header-links. Or, you may as well click on the following header-links to take you to the page discussing in detail the specific Percentages concept:

Converting percent into fraction. Multiply the given number with the fraction 1/100, which denotes the percent symbol %.

50% = 50 × (1/100) = ½

Converting fraction into percent. Multiply the given fraction with 100 and write the percent symbol % – (½) × 100 = 50%

Question:

A boy is 150 cms tall. Next year, he grew to 160 cms tall. What is the percent increase in his height?

Answer:

Growth in height is 10 cms on an initial height of 150 cms. So, percent growth is (10/150) × 100% = 6.67%. Percent Decrease.

Question:

A girl weighs 60 kg. After an exercise regimen, she weighs 55 kg 3 months later. What is the percent decreasein her weight?

Answer:

Decrease in weight is 5 kg on an initial weight of 60 kg. So, percent decrease in weight is (5/60) × 100% = 8.33%. Percent more.

Example:

A same book costs $25 in one shop and $20 in another shop. By what percent is the price of the book in the first shop more than that in the second shop?

Answer:

The price in the first shop is 5 more than 20 in the second shop. 5 more on 20 is how much more on 100 (i.e. percent more) 0.25
Remember the % more formula as below:

the percent more formula

Percent less

Example:

Two boys are 160 and 150 cms tall. How much percent is second shorter than the first?

Answer:

The second is 10 cms less than 160 (height of the first). 10 less than 160 is how much less on 100 (percent). Remember the following formula for % less

percent less formula

Overall percent change during successive percent changes:

Question:

A stock increases by 20% in 3 months. On this price, it again increases by another 10% the next month. What is overall percent increase in the stock price which is a single value equivalent of the two successive percentage increases?

Answer:

Let original price be $100. Price after the first increase of 20% on this 100 = 120. Now 10% increase on 120 is 12. Price after the second increase of 10% on this 120 = 120 +12 = 13 2. So, 100 increased to 132 results in a 32% increase. Apply the following formula to find overall % change during successive % changes: (x + y + xy/100)%

In the given question, x = 20% and y = 10%. Therefore, the overall percent increase is [20 + 10 + (20 × 10)/100]% = 32%.