To compare quantities, there are multiple methods, such as ratio and proportion, percentage, profit and loss, and simple interest.

- Prices related to an item are: (i) Selling price (ii) Cost price
**Selling price (SP)**is the price at which a product is sold out.**Cost price (CP)**is the buying price of an item.- Profit = Selling price – Cost price
- Loss = Cost price – Selling price
- If SP > CP , then it is profit.
- If SP = CP , then it is neither profit nor loss.
- If CP > SP , then it is loss.

### Percentages

Percentages are ratios expressed as a fraction of 100.

**Equivalent Ratios**

Different ratios are compared with each other to know whether they are equivalent or not. For this, we write the ratios in the form of fractions and then compare them by converting them into like fractions. If these like fractions are equal, we say that the given ratios are equivalent. Equivalent ratios are very important. Two ratios are said to be equivalent if when converted into like fractions, they are equal.

### Simple and Compound Interest

### Interest

**Interest** is the extra payment that a borrower should pay to the lender along with the principal.

### Amount

A borrower should return the principal amount (he/she has borrowed) and the interest to the lender. This money is called amount.

⇒ Amount = Principal + Interest.

### Simple Interest

Simple interest(SI) is the interest charged on a borrowed money where the principal amount will be fixed for a particular time period.

**Increase or Decrease as Percent**

There are times when we need to know what the increase in a certain quantity or decrease in it is as percent.

For example, if the population of a state is increased from 5,50,000 to 6,05,000, this could more clearly be understood if written as:

The population is increased by 10%.

NCERT Solutions