A percentage is a useful tool that can be used in everyday life. It makes the world of mathematics much more accessible to everyone because it provides shortcuts for many common tasks. For example, finding sales tax, discounts, or tip amounts is all easily done using percentages. There are some things one must keep in mind when working with percentages. However, the most important is that percentage means “out of 100%”.

## Percentages can be used for several purposes:

### 1) To compare prices over time:

Inflation makes changes in currency values relative. If a product that used to cost rs 1 in 2001 costs rs 1.35 today, this means that the price has increased by 35%. This is because, in 2001, rs 1 was worth more than 1/100 of the value of products, while now it is only worth 1/135 of such things.

### 2) To compare prices between products and determine which one offers the best deal:

Going back to our example from before, imagine there were two items on sale: an MP3 player and an iPod iSight camera for rs 18 and rs 88 respectively. While many people might be tempted at first glance to choose the cheaper option, their knowledge of percent allows them not to over-simplify such decisions. Notice that 100 – 18 is 82 and 100 – 88 is 12.

Thus the percentage decrease in price from the first product to the second was only 8% while that of the second compared to the first was 14%. This means that it makes more sense to go for the more expensive item since its savings is higher as a percent.

### 3) To find discounts, sales tax, tips, etc.

The easiest way to determine what numbers should be input would be to set up a proportion with all relevant numbers. For example, suppose we were looking for a 10% discount on an item costing rs 105 with sales tax included. We would write

(100*0.10)/100=105*0.90=9 * 105 = rs 99.50

x=99.5 rs

In this case, the best deal would be to ignore the percent and choose the item at rs 100 since one saves more money when it’s discounted than what 10% of its original value is.

This also works for other types of problems where a certain number has to be found out when given multiple different ones. For example, suppose we needed to know how much sales tax should be paid on an item worth rs 88 after a 15% discount. We could set up frac{88*0.15}{100}=\frac{88*0.85}{100}. Solving this proportion yields x=84 rs. Thus our total price becomes

88- {88*0.15}{100}=84

88-13.2=75.8 rs

Thus, rs 75.80 should be paid for this item after discounting. Note that there are several different ways to set up this problem using different numbers, but the only thing that matters is how close the target number (i.e., sales tax) is to 100%. If it’s much greater than that, then one could simply use 100 as their base value; similarly, if it’s much lower than that, you can use 1 as your base value instead.

Using any other value would make the calculation more complicated and should only be done when necessary since it may lead to mistakes where one does not take into account all the numbers.

### 4) To determine prices of items not on sale

For items that are not discounted, one needs to get prices before tax and after-tax for comparison. One then simply takes the percent difference between these two values. For example, if an item previously cost 100 before the sales tax was factored in and today it costs 105 with sales tax included, the percentage increase is {105-100}{100}=5%.

### 5) To compare two different jobs, given a percent increase in salary from one job to another

For this problem, one can set up a proportion using all relevant numbers as usual. So if he/she were offered a job where their salary was expected to rise by rs 500 with each paycheque and they were offered another job where their salary would rise by rs 1000 with each paycheque, the best option is to go for the first one.

### 6) To compare returns on investments

Suppose we have two stocks A and B that we’re considering investing in where Stock A has a 15% return and Stock B has a 20% return. We can set up a proportion using all relevant numbers as usual. For example, the best option would be to buy stock A.

This is where Cuemath comes into the scenario. Cuemath’s website solves all problems regarding how to calculate percentages which heavily influence one’s everyday life.