Question

7. If the selling price of 10 articles is the same as the cost price of 11 articles, find gain percent.
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Answer 1

Let :

• CP of one article = x
• SP of one article = y

Given :

• CP of 11 article = SP of 10 article

To find :

Gain Percentage

Formula used :

1. Profit = SP - CP
2. Profit% = Profit × 100 ÷ CP

Solution :

We know that,

$\sf \bullet \: \: Cost \: price \: of \: 1 \: article \: = \: x \\ \sf \implies \: Cost \: price \: of \: 11 \: Article \: = \: 11x$

$\sf \bullet \:Selling\:Price\: of \: 1 \: article \: = \: y \\ \sf \implies \:Selling \: Price \: of \: 10 \: article \: = \: 10y$

Also , given that ,

$\sf \bullet \: SP \: of \: 10 \: article \: = \: CP \: of \: 11 \: article \: \\ \\ \sf \implies \: 10y = 11x \\ \\ \sf \implies \: y \: = \: \dfrac{11y}{10}$

Therefore,

$\sf \bullet \:Profit \: = SP \: of \: 1 \: article \: -\: CP \: of \: 1 \: article \\ \\ \sf \implies \: Profit \: = y - x \\ \\ \sf \implies \: Profit \: = \dfrac{11x}{10} - x \\ \\ \sf \implies \: Profit \: = \dfrac{11x - (1 \times 10)x}{10} \\ \\ \sf \implies \: Profit \: = \dfrac{11x - 10x}{10} = \dfrac{x}{10}$

$\sf \bullet \:Profit \% = \: \dfrac{Profit}{CP} \times \: 100 \\ \\ \sf \implies \: Profit \% = \dfrac{ \dfrac{x}{10} }{x} \times 100 \\ \\ \sf \implies \: Profit \: \% = \: \frac{x}{10 x} \times 100 \\ \\ \sf \implies \: Profit \% = 10 \%$

ANSWER :

Gain (or Profit) % = 10%