Comparing quantities class 8 formulas

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By using these formulas you will learn about Comparing quantities.

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Comparing quantities class 8 formulas

• The discount is a reduction given on the market price. Discount = Marked Price – Selling price.
• The discount can be calculated when the 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. C.P = Buying Price + Overhead expenses
• Sales tax is charged on the sale of an item by the government and is added to the bill amount. Sales tax = Tax % of the bill amount
• Sales Tax $=\frac{\text { C.P. } \times \text { Rate of S.T. }}{100}$
  
  where
  
  M.P. = Marked Price
  
  S.P. = Selling Price
  
  M.P = S.E + Discount
  
  Discount = M.P – S.P



• Discount $\%=\frac{\text { Discount } \times 100}{\text { M.P. }}$
• When profit % is given, then S.P > C.P and
  
  S.P. $=\left(\frac{100+\text { Profit } \%}{100}\right) \times$ C.P
  
  C.P. $=\frac{\text { S.P. } \times 100}{100+\text { Profit } \%}$
  
  Profit $=\frac{\text { Profit } \% \times \text { C.P. }}{100}$
  
  Profit (gain) $=$ S.P. $-$ C.P.
  
  Profit $\%=\frac{\text { Profit }}{\text { C.P. }} \times 100$



• When loss % is given S.P < C.P and
  
  S.P. $=\frac{100-\text { Loss } \%}{100} \times$ C.P.
  
  C.P. $=\frac{\text { S.P. } \times 100}{100-\text { Loss } \%}$
  
  Loss $=\frac{\text { Loss } \% \times \text { C.P. }}{100}$
  
  Loss $=$ C.P. $-$ S.P.
  
  Loss $\%=\frac{\text { Loss }}{\text { C.P. }} \times 100$



• Increase and Decrease Percent
  
  Increase $\%=\left(\frac{\text { Increase }}{\text { Original value }} \times 100\right) \%$
  
  Decrease $\%=\left(\frac{\text { Decrease }}{\text { Original value }} \times 100\right) \%$

Simple Interest(SI):

When the interest is paid to the lender regularly every year or half year on the same interest, we call it a simple interest. In other words, interest is said to simple, if it is calculated on the original principle throughout the loan period.

$S . I .=\frac{P \times R \times T}{100}$

Where, $\mathrm{P}=$ Principal, $\mathrm{R}=$ Rate of Interest, $\mathrm{T}=$ Time .

Compound Interest (CI):

If the borrower and the lender agree to fix up a certain interval of time (say, a year or a half-year or a quarter of a year, etc.), so that the amount at the end of an interval becomes the principal for the next-interval, then the total interest over all the intervals calculated in this way is called the compound interest. Also, CI = Amount – Principal

(a) When interest is compounded annually, then

Amount $A=P\left(1+\frac{R}{100}\right)^{n}$ and $\mathrm{CI}=\mathrm{A}-\mathrm{P}=\mathrm{P}\left\{\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}-1\right\}$

where P is Principal, R is the rate of interest and n is time period.

(b) When Interest is Compounded Half-Yearly, then

Amount $A=P\left(1+\frac{R}{2 \times 100}\right)^{2 n}$

where $\left\{\begin{array}{l}\frac{\mathrm{R}}{2} \text { is half yearly rate and } \\ 2 n=\text { number of half-years }\end{array}\right.$

and $C I=A-P=P\left\{\left(1+\frac{R}{2 \times 100}\right)^{2 n}-1\right\}$

When R₁, R₂ and R₃ are different rates for the first, second and third year, then

Amount $A=P\left(1+\frac{R_{1}}{100}\right)\left(1+\frac{R_{2}}{100}\right)\left(1+\frac{R_{3}}{100}\right)$

and $C I=A-P=P\left\{\left(1+\frac{R_{1}}{100}\right)\left(1+\frac{R_{2}}{100}\right)\left(1+\frac{R_{3}}{100}\right)-1\right\}$

Also Read,

Download NCERT Class 8 Maths Book in PDF 

Download NCERT Class 8 Science Book in PDF

Download NCERT Class 8 Science Exemplar in PDF

Download NCERT Class 8 Maths Exemplar in PDF

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