Question

If the selling price of 20 articles is equal to the cost price of 23 articles, find the loss or gain percent for each article.​

Answer 1

Solution :

The selling price of 20 articles is equal to the cost price of 23 articles.

Let this be equal to k

Selling price of 1 article is (k/20)

Cost price of 1 article is (k/23)

It is obvious that the cost price is lesser than the selling price.

So, it's a profit

Profit per article

>> (k/20) - (k/23)

>> 3k/460

Profit percentage

>> (3k/460)/(k/23) × 100%

>> (3k/460) × (23/k) × 100%

>> (3/20) × 100%

>> 15%.

Answer : The overall gain percentage is 15% .

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

Answer 2

$\color{teal} \underbrace{ \bf Given \: Information :-}$

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• Selling price of 20 articles and cost price of 23 articles are equal

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$\color{maroon} \underbrace{ \bf To \: Find :-}$

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• The loss or gain percent per articles

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$\bf\color{magenta}{\underbrace { Formula \: Used : - }}$

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$\qquad \bull \: \: \underline{ \boxed {\sf Profit \: \% = \frac{profit}{cost \: price} \times 100}}$

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$\bf \color{orange} \underbrace{Solution :-}$

Let the price of each article be k. Therfore, according to the provided information, we get :-

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$\bull \: \sf Cost \: Price \: of \: each \: article = \dfrac{k}{23}$

$\bull \: \sf Selling \: Price \: of \: each \: article = \dfrac{k}{20}$

Now, here we see that, the deal is of profit i.e. Selling price is more than cost price. Therefore it's a profit. Thus :-

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$\sf : \longrightarrow profit = \dfrac{k}{20} - \dfrac{k}{23} \: \: \: \\ \\ \sf : \longrightarrow profit = \frac{23k - 20k}{460} \\ \\\sf : \longrightarrow profit = \frac{3k}{460} \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Therefore now using the formula for profit percent. We have :-

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$\sf : \longrightarrow profit \: \% \: = \dfrac{ \dfrac{3k}{460} }{ \dfrac{k}{23} } \times 100 \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longrightarrow profit \: \% \: = \frac{3k}{460} \times \frac{23}{k} \times 100 \\ \\ \sf : \longrightarrow profit \: \% \: = \frac{ \green{ \cancel{3k}}}{ \blue{ \cancel{460}} } \times \frac { \blue{\cancel{23}}}{ \green{ \cancel{k} }} \times 100 \\ \\ \sf : \longrightarrow profit \: \% \: = \frac{3}{ \red{ \cancel{20} }}\times \red{\cancel{ 100}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longrightarrow profit \: \% \: =3 \times 5 = 15 \: \% \: \: \: \: \: \: \: \:$