Question

make a list of all the formulae used in chapter 8 comparing quantities​

Answer 1

$\large\underline{\sf{Solution-}}$

1. Profit and Loss

$\red{ \boxed{ \sf{ \:Profit = SP - CP}}}$

$\red{ \boxed{ \sf{ \:Profit\% = \frac{Profit}{CP} \times 100\%}}}$

$\red{ \boxed{ \sf{ \:SP = \frac{(100 + Profit\%) \times CP}{100}}}}$

$\red{ \boxed{ \sf{ \:CP = \frac{100 \times SP}{100 + Profit\%}}}}$

$\red{ \boxed{ \sf{ \:Loss = CP - SP}}}$

$\red{ \boxed{ \sf{ \:Loss\% = \frac{Loss}{CP} \times 100\%}}}$

$\red{ \boxed{ \sf{ \:SP = \frac{(100 - Loss\%) \times CP}{100}}}}$

$\red{ \boxed{ \sf{ \:CP = \frac{100 \times SP}{100 - Loss\%}}}}$

2. Marked Price and Discount

$\red{ \boxed{ \sf{ \:SP = MP - Discount}}}$

$\red{ \boxed{ \sf{ \:Discount\% = \frac{Discount}{MP} \times 100\%}}}$

$\red{ \boxed{ \sf{ \:SP = \frac{(100 - Discount\%) \times MP}{100}}}}$

$\red{ \boxed{ \sf{ \:MP = \frac{100 \times SP}{100 - Discount\%}}}}$

3. Sale Tax

$\red{ \boxed{ \sf{ \:SP = LP + Sale \: tax}}}$

$\red{ \boxed{ \sf{ \:Sale \: tax \: \% = \dfrac{Sale \: tax \:}{LP} \times 100\%}}}$

4. VAT

$\red{ \boxed{ \sf{ \:SP = LP + VAT}}}$

$\red{ \boxed{ \sf{ \:VAT \: \% = \dfrac{VAT \:}{LP} \times 100\%}}}$

5. Compound interest

Amount on a certain sum of Rs p invested at the rate of r % per annum compounded annually for n years is

$\red{ \boxed{ \sf{ \:Amount = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n}}}}$

Amount on a certain sum of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\red{ \boxed{ \sf{ \:Amount = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n}}}}$

Amount on a certain sum of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\red{ \boxed{ \sf{ \:Amount = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n}}}}$

And

Compound interest on a certain sum of Rs p invested at the rate of r % per annum compounded annually for n years is

$\red{ \boxed{ \sf{ \:CI = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} - p}}}$

Compound interest on a certain sum of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\red{ \boxed{ \sf{ \:CI = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} - p}}}$

Compound interest on a certain sum of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\red{ \boxed{ \sf{ \:CI = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} - p}}}$

Value on a certain sum of Rs p depreciated at the rate of r % per annum compounded annually for n years is

$\red{ \boxed{ \sf{ \: Value = p {\bigg[1 - \dfrac{r}{100} \bigg]}^{n}}}}$

Answer 2

Step-by-step explanation:

Topics are

1. SP and CP

2. Sale Tax

3. Vat

4. Compound Interest

5. Depreciation