Question

When a car is sold for rupees 36000, the loss is 10%. What is the cost price of the car?

Answer 1

Given:

A car with -

• Selling Price = Rs. 36000.
• Loss % = 10 %

What To Find:

We have to -

• Find the cost price of a car.

Formula Needed:

The formula is -

$\bf CP = \dfrac{SP \times 100}{100 - Loss \: \%}$

Abbreviation Used:

• CP = Cost Price
• SP = Selling Price

Solution:

Using the formula,

$\sf \implies CP = \dfrac{SP \times 100}{100 - Loss \: \%}$

Substitute the values,

$\sf \implies CP = \dfrac{36000 \times 100}{100 - 10 \: \%}$

Solve the numerator,

$\sf \implies CP = \dfrac{3600000}{100 - 10 \: \%}$

Solve the denominator,

$\sf \implies CP = \dfrac{3600000}{90}$

Divide 3600000 by 90,

$\sf \implies CP =40000$

Final Answer:

∴ Thus. the cost price of the car is Rs. 40000.

Answer 2

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{darkblue}{Given:}}}}}}}\end{gathered}$

• $\dashrightarrow{\sf{Selling \: Price \: of \: Car = 36000}}$
• $\dashrightarrow \sf{Loss \% = 10 \%}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{darkblue}{To Find:}}}}}}}\end{gathered}$

• $\dashrightarrow{\sf{Cost \: Price \: of \: car}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{darkblue}{Using Formula:}}}}}}}\end{gathered}$

$\dag{\underline{\boxed{\sf{C.P = {\bigg\{}{\dfrac{S.P \times 100}{100 - Loss \: \%}}{\bigg\}}}}}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{darkblue}{Solution:}}}}}}}\end{gathered}$

$\dag \: {\underline{\pmb{\frak{\red{Finding \: the \: Cost \: price \: by \: using \: formula }}}}}$

$\quad{: \implies{\sf{C.P = \bf{\dfrac{S.P \times 100}{100 - Loss \: \%}}}}}$

• Substituting the values

$\quad{: \implies{\sf{CP = \bf{\dfrac{ 36000 \times 100}{100 - 10}}}}}$

$\quad{: \implies{\sf{CP = \bf{\dfrac{ 36000 \times 100}{90}}}}}$

$\quad{: \implies{\sf{CP = \bf{\dfrac{ 3600000}{90}}}}}$

$\quad{: \implies{\sf{CP = \bf{\cancel{\dfrac{3600000}{90}}}}}}$

$\quad{: \implies{\sf{CP = \bf{40000}}}}$

$\begin{gathered} \dag{\overline{\underline{\boxed{\bf{\color{red}{CP=40000}}}}}}\end{gathered}$

$\therefore{\underline{\sf{Cost \: Price \: of \: car \: is \: Rs.40000...}}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{darkblue}{Know More:}}}}}}}\end{gathered}$

$\boxed{\begin{minipage}{5cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf {\textcircled{\footnotesize\textsf{1}}} \:S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100 \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}} \: \: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}\begin{gathered}\large\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P - C.P} \\ \\ \bigstar \:\sf{Loss = C.P - S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100 - loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100 - loss\%} \times S.P}\end{array} }\end{gathered}\end{gathered}$