Question

if an object is sold at rs 500, there is a lose of 5%. At what price it should be sold to gain a profit of 5%. (answer for these question is rs 552.64 please solve) ​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{SP = Rs. \:500}\\\sf{Loss\% = 5\%}\\ \sf{CP=?}\end{cases}$

• Calculation of Cost Price of Object :

$\longrightarrow \tt SP = CP \times (100 - Loss)\% \\ \\\longrightarrow \tt 500 = CP \times (100 - 5)\% \\ \\\longrightarrow \tt 500 = CP \times 95\% \\ \\\longrightarrow \tt 500 = CP \times \dfrac{95}{100} \\ \\\longrightarrow \tt 500 \times \cancel\frac{100}{95} = CP \\ \\\longrightarrow \tt CP = \dfrac{500 \times 20}{19}\\ \\\longrightarrow\blue{\tt CP =Rs.\: \dfrac{10000}{19}}$

$\rule{300}{1}$

$\bf{ Given}\begin{cases}\sf{CP= Rs. \:\dfrac{10000}{19} }\\\sf{Profit\% = 5\%}\\\sf{SP=?}\end{cases}$

• Calculation of New Selling Price :

$\longrightarrow \tt SP = CP \times (100 + Profit)\% \\ \\\longrightarrow \tt SP = \dfrac{10000}{19} \times (100 + 5)\% \\ \\\longrightarrow \tt SP = \dfrac{10000}{19} \times 105\% \\ \\\longrightarrow \tt SP = \dfrac{100 \cancel{00}}{19} \times \dfrac{105}{\cancel{100}}\\ \\\longrightarrow \tt SP =\dfrac{100}{19} \times 105 \\ \\\longrightarrow \tt SP = \cancel\dfrac{10500}{19} \\ \\\longrightarrow \large \boxed{ \red{\tt SP =Rs. \:552.64}}$

⠀

∴ Therefore, Object should be sold at Rs. 552.64 to gain 5% Profit on it.

$\rule{300}{2}$

• S H O R T C U T ⠀T R I C K :

$\implies \tt New \:SP = \dfrac{Old \:SP \times Event_2}{Event_1} \\ \\\implies \tt New \:SP = \dfrac{500 \times (100 + 5)\%}{(100 - 5)\%} \\ \\\implies \tt New \:SP = \dfrac{500 \times 105 \cancel{\%}}{95\cancel{\%}} \\ \\\implies \tt New \:SP = \dfrac{500 \times 105}{95} \\ \\\implies \tt New \:SP = \cancel\dfrac{52500}{95} \\ \\ \implies\large \boxed{ \red{\tt SP =Rs. \:552.64}}$

⠀

∴ Therefore, Object should be sold at Rs. 552.64 to gain 5% Profit on it.

$\rule{300}{3}$

$\boxed{\begin{minipage}{7 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

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Answer 2

Question :

If an object is sold at Rs 500, there is a loss of 5%. At what price it should be sold to gain a profit of 5%. (answer for these question is rs 552.64 please solve)

Solution :

$\underline{\bold {Given:}}$

• Selling Price=Rs 500
• Loss%=5%

$\underline{\bold {To\:Find:}}$

• Selling price to gain a profit of 5%.

$\boxed{\blue{Cost \: Price =( \frac{100}{100-Loss\%} \times Selling Price ) }}$

$\implies Cost \: Price =( \frac{100}{100 -Loss\%} \times Selling Price ) \\ \implies Cost \: Price = Rs \: (\frac{100}{100 - 5 } \times 500) \\ \implies Cost \: Price = Rs \: ( \frac{100}{95} \times 500) \\\implies Cost \: Price = Rs \:(\frac{20\times 500}{19})\\\implies Cost\:Price= Rs \:(\frac{10000}{19})$

$\rule{193}{1}$

$\boxed{\pink{Selling \: Price =( \frac{100+Profit\%}{100} \times Cost\:Price )}}$

$\implies Selling \: Price =(\frac{100+Profit\%}{100} \times Cost\:Price)\\\implies Selling \: Price=Rs\:(\frac{100+5}{100} \times \frac{10000}{19})\\\implies Selling \: Price =Rs\:(\frac{105}{100} \times \frac{10000}{19})\\\implies Selling \: Price =Rs\:(\frac{100\times 105}{19})\\\implies Selling \:Price=Rs\:552.64$

$\boxed {\green{\therefore{The \:required \:selling\: price =Rs\:552.64}}}$

$\rule {193}{2}$

#AnswerWithQuality

#BAL