Students can go through AP Board 8th Class Maths Notes Chapter 5 Comparing Quantities Using Proportion to understand and remember the concepts easily.

## AP State Board Syllabus 8th Class Maths Notes Chapter 5 Comparing Quantities Using Proportion

→ Two simple ratios are expressed like a single ratio as the ratio of product of antecedents to product of consequents and we call it compound ratio of the given two simple ratios.

a : b and c : d are any two ratios, then their compound ratio is \(\frac{a}{b}\) × \(\frac{c}{d}\) = \(\frac{ac}{bd}\) i.e. ac : bd.

→ A percentage(%) compares a number to 100. The word percent means “per every hundred” or “out of every hundred”. 100% = \(\frac{100}{100}\) it is also a fraction with denominator 100.

→ Discount is a decrease percent of marked price. Price reduction is called rebate or discount. It is calculated on marked price or list price.

→ Profit or loss is always calculated on cost price. Profit is an example of increase percent of cost price and loss is an example of decrease percent of cost price.

→ VAT will be charged on the selling price of an item and will be included in the bill.

VAT is an increase percent on selling price.

→ Simple interest is an increase percent on the principal.

→ Simple interest (I) = \(\frac{P \times T \times R}{100}\)

where P = Principal, T = Time inyears, R = Rate of interest.

→ Amount = Principal + Interest = P + \(\frac{P \times T \times R}{100}\) = P\(\left(1+\frac{T \times R}{100}\right)\)

→ Compound interest allows you to earn interest on interest.

→ Amount at the end of ‘n’ years using compound interest is A = P \(\left(1+\frac{R}{100}\right)^{n}\)

→ The time period after which interest is added to principal is called conversion period.

When interest is compounded halfyearly, there are two conversion periods in a year, each after 6 months. In such a case, ha If year rate will be half of the annual rate.

→ Note: 1.615 : 1 is called as golden ratio.

In ancient Greece, artists and architects believed there was a particular rectangular shape that looked very pleasing to the eye. For rectangles of this shape, the ratio of long side to the short side is roughly 1.615 : 1. This ratio is very close to what is known as golden ratio.