# Percentage and Applications

A fraction whose denominator is 100 is read as percent, for example 23/100 is read as twenty three percent or 23%. The symbol % is used for the term percent.

**Percentage:** Percent means per every hundred and denoted by the symbol %. A fraction with denominator 100 is called a Percent.

**Percent as a fraction: **Drop the % sign and multiply the given number by 1/100 and simplify it.

**Percent as a decimal:** Drop the % sign and insert or move the decimal point two places to the left.

**Fraction as a percent:** Multiply the fraction by 100, simplify it and mark % sign.

**Decimal as a percent: **Shift the decimal point two places to the right and mark % sign.

### Profit and Loss

**Cost Price (cp):** Amount paid to buy an article.

**Selling Price (sp):** Amount at which an article is sold.

**Profit or Gain:** When sp > cp, the seller makes a profit or gain.

Gain = sp - cp

**Loss: **When cp > sp, the seller incurs a loss.

Loss = cp - sp

Gain and loss are always calculated on the cp.

**Gain %** = (Gain x 100)/cp

**Loss %** = (Loss x 100)/cp

### Discounts

**Marked price or list price (MP):** Price at which a article is listed for sale.

**Discount:** Reduction in the marked price of an article.

**Net selling price (SP): **SP = MP - Discount

### Interests

**Principal (P):** Money borrowed

**Interest (I):** Extra or additional money paid by the borrower.

**Simple Interest (SI):** Interest which is calculated uniformly on P throughout the loan period.

SI = (p x r x t)/100

**Amount (A):** Total money paid by the borrower.

A = P + I or I = A - P

**Rate (R):** Interest on Rs.100 for 1 year is known as the rate percent per annum.

**Compound Interest (CI):** Interest obtained during the first time period is added to the original P and amount becomes new P for the second time period and so on. The difference between the amount obtained at the last time period and original principal is called compound interest.

$$ A = P \left (1 + \frac{R}{100} \right )^t $$