Question

How much percent above the cost price should a shopkeeper mark his good so that after allowing a discount of 20 percent on the marked price he gains 12 percent

Answer 1

40% is the answer ♥️♥️

Answer 2

$\underline\mathfrak{Given:-}$

• $\: \: \: \: \: \: \: Discount \: \: \leadsto \: \: {20} \: \%$
• $\: \: \: \: \: \: \: Gain \: \: on \: \: marked \: \: price \: \: \leadsto \: \: {12} \: \%$

$\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: percent \: \: above \: \: the \: \: cast \: \: price \: \: should \: \: a \: \: shopkeeper \: \: marks \\ \: \: \: \: \: So \: \: that \: \: after \: \: allowing \: \: discount \: \: of \: \: {20} \: \% \: \: on \: \: MRP \: \: he \: \: gain \: \: {12} \: \%$

$\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: \: \: Let \: \: the \: \: cast \: \: price \: \: be \: \: {100} \: \: and \: \: marked \: \: price \: \: be \: \: x$

$\: \: \: \: \: \therefore Gain \: \: \leadsto \: \: {12} \: \% \: \: of \: \: {100}$

$\: \: \: \: \: \leadsto {12} \: \times \: \frac{100}{100}$

$\: \: \: \: \: \leadsto \: Rs \: {12}$

$\: \: \: \: \: \therefore Selling \: \: price \: \: \leadsto \: \: Cost \: \: price \: + \: Gain$

$\: \: \: \: \: \leadsto {100} \: + \: {12}$

$\: \: \: \: \: \leadsto \: Rs \: {112}$

$\: \: \: \: \: \therefore Discount \: \: \leadsto \: \: {20} \: \% \: \: of \: \: x$

$\: \: \: \: \: \leadsto \: \: x \: \times \frac{20}{100}$

$\: \: \: \: \: \leadsto \frac{20}{100}$

$\: \: \: \: \: \therefore Selling \: \: price \: \: = \: \: marked \: \: price \: \: discount.$

$\: \: \: \: \: \leadsto {x} \: - \: \frac{x}{5} \: \: = \: \: {112}$

$\: \: \: \: \: \leadsto \frac{{5x} \: - \: {x}}{5} \: \: = \: \: {112}$

$\: \: \: \: \: \leadsto \frac{4x}{5} \: \: = \: \: {112}$

$\: \: \: \: \: \leadsto {4x} \: \: = \: \: {112} \: \times \: {5}$

$\: \: \: \: \: \leadsto {4x} \: \: = \: \: {560}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: \frac{560}{4}$

$\: \: \: \: \: \leadsto {x} \: \: = \: \: {140}$

• $\: \: \: \: \: Hence, \: \: marked \: \: price \: \: = \: \: Rs \: {140}$

$\: \: \: \: \: \therefore Amount \: \: marked \: \: above \: \: the \: \: cost \: \: price:-$

$\: \: \: \: \: \leadsto {140} \: - \: {100}$

$\: \: \: \: \: \leadsto {40}$

$\: \: \: \: \: Now,$

$\: \: \: \: \: \therefore percentage \: \: of \: \: marked \: \: price:-$

$\: \: \: \: \: \leadsto \: \: {40} \: \times \frac{100}{100}$

$\: \: \: \: \: \leadsto {40} \: \%$

• $\: \: \: \: \: Hence, \: \: the \: \: marked \: \: price \: \: is \: \: {40} \: \% \: \: above \: \: the \: \: cast \: \: price.$

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