Question

An article was sold for Rs 550 with a profit of 5 % . What was its cost price​

Answer 1

Answer :-

Given :-

• Selling price = Rs. 550
• Profit percentage = 5%

To Find :-

• Cost price

Solution :-

We know that,

$\sf Cost \:price = \dfrac{100}{100 + Profit\%} \times SP$

Substituting the values :-

$\implies\sf CP = \dfrac{100}{100 +5} \times 550$

$\implies\sf CP = \dfrac{100}{105} \times 550$

$\implies\sf CP = \dfrac{20}{21} \times 550$

$\implies\sf CP \approx 523.8$

Cost price = Rs. 523.8

Additional information :-

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

Answer 2

Given :

• Selling Price (S.P) = Rs 550
• Profit % = 5%

To Find :

• Cost Price (C.P)

Formula :

${\underline{\boxed {\mathcal{\pmb{\quad C.P \: = \: \dfrac{100}{ \: 100 \: + \: Gain\%} \: \times \: S.P\quad}}}}}$

Solution :

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

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: + \: 5} \: \times \: 550 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 105} \: \times \: 550 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: \cancel{105}} \: \times \: \cancel{550} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100\: \times \: 110}{ \: 21} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{11000}{ \: 21} }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{C.P \: = \: Rs 523.80}}$

Thus Cost Price of Article is Rs 523.80

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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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