### Comparing Quantities - Revision Notes

CBSE Class 8 Mathematics
Revision Notes
Chapter – 8
Comparing Quantities

• Ratio: Comparing by division is called ratio. Quantities written in ratio have the same unit. Ratio has no unit. Equality of two ratios is called proportion.
• Product of extremes = Product of means
• Percentage: Percentage means for every hundred. The result of any division in which the divisor is 100 is a percentage. The divisor is denoted by a special symbol %, read as percent.
• Profit and Loss:
(i)  Cost Price (CP): The amount for which an article is bought.
(ii)  Selling Price (SP): The amount for which an article is sold.
• Additional expenses made after buying an article are included in the cost price and are known as overhead expenses. These may include expenses like amount spent on repairs, labour charges, transportation, etc.
• Discount is a reduction given on marked price.  Discount = Marked Price – Sale Price.
• Discount can be calculated when discount percentage is given.  Discount = Discount % of Marked Price
• Simple Interest: If the principal remains the same for the entire loan period, then the interest paid is called simple interest. $SI=\frac{P×R×T}{100}$
(i) Amount when interest is compounded annually $=P\left(1+\frac{R}{100}{\right)}^{n}$ P is principal, R is rate of interest, n is time period
$=P\left(1+\frac{R}{100}{\right)}^{2n}$$\left[\frac{R}{2}is,\phantom{\rule{thickmathspace}{0ex}}half\phantom{\rule{thickmathspace}{0ex}}yearly\phantom{\rule{thickmathspace}{0ex}}rate\phantom{\rule{thickmathspace}{0ex}}and\phantom{\rule{thickmathspace}{0ex}}2n$