Question

A trader bought an article for Rs x and sold it for Rs 52, thereby making a profit of x-10 percent on his outlay.calculate the cost price.

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Cost Price of an Article is Rs x

Selling Price of an Article is Rs 52

Profit % = (x - 10) %

Now, We know,

Relationship between Selling Price, Cost Price and Profit % is connected by

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

So, on substituting the values, we get

$\rm \: 52 = \dfrac{(100 + x - 10) \times x}{100}$

$\rm \: 52 = \dfrac{(90 + x) \times x}{100}$

$\rm \: x(90 + x) = 5200$

$\rm \: 90x + {x}^{2} = 5200$

can be rewritten as

$\rm \: {x}^{2} + 90x - 5200 = 0$

On splitting the middle terms, we have

$\rm \: {x}^{2} + 130x - 40x - 5200 = 0$

$\rm \: x(x + 130) - 40(x + 130) = 0$

$\rm \: (x + 130)(x - 40) = 0$

$\rm\implies \:x = 40 \: \: or \: \: x \: = \: - 130 \: \{rejected \}$

Hence,

Cost Price of an Article = Rs 40

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$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Given Data :

Cost price of an Article is Rs.x

Selling Price of an Article is Rs.52

Profit % = (x - 10)%

To Find :

Cost Price of that Article.

Solution :

By using,

S.P = [(100 + Profit%) x C.P]/100

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⇒ 52 = [ (100 + x - 10) × (x) ]/100

⇒ 5200 = 90x + x²

⇒ x² + 90x - 5200 = 0

• By using splitting middle term method

⇒ x² + 130x - 40x - 5200 = 0

⇒ x(x + 130) - 40(x + 130) = 0

⇒ (x + 130) (x - 40) = 0

⇒ x = 40 , -130(reject)

∵ cost price can't be in Negative.

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∴ Cost of the Article = Rs.40