Question

A man sold an article at Rs. 2500 and got a loss of 5%. What is the cost price of the article?​

Answer 1

Answer:

Given, C.P.=Rs2,500

and S.P. =125 % of C.P.=100125×2,500=Rs3,125 

As 4 % of the S.P. is paid as tax,  amount paid as tax =1004×3,125=Rs125

So, actual Profit =S.P.−C.P.−tax=Rs3,125−Rs2,500−125=Rs500

Answer 2

Given :

• Selling Price (S.P) = Rs 2500
• Loss % = 5%

To Find :

• Cost Price of Article

Formula :

$\blue \bigstar \: {\underline \red{\boxed {\mathcal{\pmb{ \color{orange}{\quad C.P \: = \: \dfrac{100}{ \: 100 \: - \: Loss \%} \: \times \: S.P}\quad}}}}}$

Solution :

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

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: - \: 5} \: \times \: 2500 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 95} \: \times \: 2500 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100 \: \times \: 2500}{ \:95 } } }$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{250000}{ \: 95} }}$

$\qquad \quad {:} \longrightarrow \sf \blue{\boxed{ \color{aqua} \bf{C.P \: = \: Rs \: 2631.57}}} \: \: \purple\bigstar..$

Thus Cost Price of Article is Rs 2631.57

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

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