These comprehensive RBSE Class 8 Maths Notes Chapter 8 Comparing Quantities will give a brief overview of all the concepts.

→ The word ‘percent’ means in every hundred or per hundred.

→ To convert a fraction into percentage, we multiply it by 100.

→ To convert percentage into fraction, we divide the number by 100.

→ Cost Price (C.P.): The price for which an article is bought is called cost price.

→ Selling Price (S.P.) is the price for which an article is sold.

→ Profit: When S.P. > C.P., then there is a profit.

Profit = S.P. - C.P.

→ Loss: When S.P. < C.P., then there is a loss.

Loss = C.P. - S.P.

→ Profit % = \(\frac{\text { Profit } \times 100}{\text { C.P. }}\)

→ Loss % = \(\frac{{Loss} \times 100}{\text { C.P. }}\)

→ S.P = \(\frac{(100+\text { Profit \%) } \times \text { C.P. }}{100}\) or \(\frac{(100-\text { Loss } \%) \times \text { C.P. }}{100}\)

→ C.P. = \(\frac{\text { SP. } \times 100}{100+\text { Profit } \%}\) or \(\frac{\text { SP. } \times 100}{100-\text { Loss } \%}\)

→ Discount is a reduction given on marked price

Discount = Marked Price - Sell Price

→ Discount can be calculated when discount percentage is given.

Discount = Discount % of Marked Price.

→ Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

CP. = Buying price + Overhead expenses.

→ Sales tax is charged on the sell of an item by the government and is added to the bill amount.

Sales tax = Tax % of Bill Amount.

→ Compound interest is the interest calculated on the previous year’s amount.

A = P + I

→ Amount when interest is compounded annualy

= P\(\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}\) P is principal, R is rate of interest, n is time period.

→ Amount when interest is compounded half yearly

= P\(\left(1+\frac{R}{200}\right)^{2 n} \) { \({\frac{R}{2}}\)is half yearly rate, 2n = number of half years.}

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