Question

A shopkeeper bought 2 TV sets ar 210,000 each. He sold one at a profit of 10% and the other at a loss of 5%. Find whether he made an overall profit or loss and by how much.​

Answer 1

Answer:

Given :

• A shopkeeper bought 2 TV sets ar 210,000 each.
• He sold one at a profit of 10% and the other at a loss of 5%.

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

To Find :

• Profit or loss

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

Using Formulas :

$\longrightarrow{\small\underline{\boxed{\sf{S.P = \dfrac{100 + Profit \% }{100} \times C.P }}}}$

$\longrightarrow{\small\underline{\boxed{\sf{S.P = \dfrac{100 - Loss\% }{100} \times C.P }}}}$

$\longrightarrow{\small{\underline{\boxed{\sf{Profit = S.P - C.P}}}}}$

⚘ Where :-

• S.P = Selling Price
• C.P = Cost Price

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

Solution :

⚘ Finding the Selling Price of a tv with 10% profit :-

$\dashrightarrow{\small{\sf{S.P = \dfrac{100 + Profit \% }{100} \times C.P }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{100 + 10 }{100} \times 210000 }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{110}{100} \times 210000 }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{110}{\cancel{100}} \times \cancel{210000} }}}$

$\dashrightarrow{\small{\sf{S.P = 110 \times 2100 }}}$

$\dashrightarrow{\small{\sf{S.P = Rs.231000}}}$

∴ The selling price of 1st tv is Rs.231000.

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⚘ Finding the Selling Price of 2nd tv with 5% loss :-

$\dashrightarrow{\small{\sf{S.P = \dfrac{100 - Loss\% }{100} \times C.P }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{100 - 5 }{100} \times 210000 }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{95 }{100} \times 210000 }}}$

$\dashrightarrow{\small{\sf{S.P = \dfrac{95}{\cancel{100}} \times \cancel{210000} }}}$

$\dashrightarrow{\small{\sf{S.P = 95\times 2100 }}}$

$\dashrightarrow{\small{\sf{S.P = Rs.199500}}}$

∴ The selling price of 2nd tv is Rs.199500.

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⚘ Finding total cost price of both tv set :-

$\dashrightarrow{\small{\sf{C.P = 210000 + 210000}}}$

$\dashrightarrow{\small{\sf{C.P =Rs.420000}}}$

∴ The cost price of both tv sets is Rs.420000.

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⚘Finding total selling price of both tv sets.

$\dashrightarrow{\small{\sf{S.P = 231000 + 199500}}}$

$\dashrightarrow{\small{\sf{S.P =Rs.430500}}}$

∴ The selling price of both tv sets is Rs.430500.

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⚘ Now, checking the shopkeeper mad profit or loss by selling the 2 tv sets :-

$\dashrightarrow\sf{S.P > C.P}$

$\dashrightarrow\sf{Profit = S.P > C.P}$

∴ The shopkeeper made profit by selling the set of 2 tv.

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⚘ Now, finding the profit by selling the 2 tv sets.

$\dashrightarrow\sf{Profit = S.P - C.P}$

$\dashrightarrow\sf{Profit = 430500 - 420000}$

$\dashrightarrow\sf{Profit = Rs.10500}$

∴ The profit by selling the tv sets is Rs.10500.

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

Learn More :

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

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