If you want to improve your class 8 Math, Comparing quantities concepts, then it is super important for you to learn and understand all the formulas.

By using these formulas you will learn about Comparing quantities.

With the help of these formulas, you can revise the entire chapter easily.

## 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 R

_{1}, R

_{2}and R

_{3}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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