Question

If SP of an article at loss of 30% is Rs 42 the CP of article is​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Selling Price = Rs. 42
• loss = 30%

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Cost price = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{Cost\: price = \dfrac{100}{100-loss}\times SP}}}}$

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$\sf:\implies \: {\bold{ CP = \dfrac{100}{70} \times 42 }}$

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$\sf:\implies \: {\bold{ CP = \dfrac{10}{7} \times 42 }}$

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$\sf:\implies \: {\bold{ CP = 10 \times 6 }}$

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$\sf:\implies \: {\bold{ CP = Rs. 60 }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Cost price of an article = Rs. 60

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Verification :-

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$\sf{\red{\boxed{\bold{Loss = CP - SP}}}}$

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loss = 60 - 42

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loss = Rs. 18

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$\sf{\red{\boxed{\bold{loss\% = \dfrac{loss}{CP}\times 100}}}}$

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$\sf:\implies \: {\bold{ loss\% = \dfrac{18}{60} \times 100 }}$

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$\sf:\implies \: {\bold{ loss\% = \dfrac{18}{6} \times 10 }}$

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$\sf:\implies \: {\bold{ loss\% = 3 \times 10}}$

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$\sf:\implies \: {\bold{ loss\% = 30\% }}$

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....Hence Verified

Answer 2

$\sf{\bold{\purple{\star{\underline{\underline{Given}}}}}}$

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• Selling price of article = Rs. 42
• Loss % = 30%

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$\sf{\bold{\purple{\star{\underline{\underline{To\: find }}}}}}$

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• cost price of article = ??

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$\sf{\bold{\purple{\star{\underline{\underline{Solution}}}}}}$

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• let the CP be x

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$\sf{\bold{\orange{\star{\underline{\underline{Loss = CP - SP}}}}}}$

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Loss = x - 42

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$\sf{\bold{\orange{\star{\underline{\underline{Loss\% = \dfrac{loss}{CP}\times 100}}}}}}$

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$\sf:\implies \: {\bold{ 30 = \dfrac{x - 42}{x}\times 100 }}$

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$\sf:\implies \: {\bold{ 30x = ( x - 42 ) \times 100 }}$

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$\sf:\implies \: {\bold{ 30x = 100x - 4200}}$

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$\sf:\implies \: {\bold{ 30x + 4200 = 100x}}$

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$\sf:\implies \: {\bold{ 4200 = 100x - 30x }}$

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$\sf:\implies \: {\bold{ 4200 = 70x }}$

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$\sf:\implies \: {\bold{ x = \dfrac{4200}{70} }}$

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$\sf:\implies \: {\bold{ x = \dfrac{420}{7} }}$

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$\sf:\implies \: {\bold{ x = Rs. 60 }}$

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Cost Price = Rs. 60