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.

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