A shopkeeper sold first unit of an article to Aria at 20% discount and the second unit of the same article at 40% discount. If the shopkeep…
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A shopkeeper sold first unit of an article to Aria at 20% discount and the second unit of the same article at 40% discount. If the shopkeeper earned an overall profit of 5%, the marked price of the article was what percent of the cost price of the article ?
Solution
Let the cost price of each article = Rs. $100x$
=> C.P. of both articles = $2 \times 100x = 200x$
=> Selling price = $\frac{105}{100} \times 200x = 210x$ ------------------Eqn(1)
Let the marked price = Rs. $100y$
Selling price of 1st article after 20% discount = $\frac{80}{100} \times 100y = 80y$
Selling price of 2nd article after 40% discount = $\frac{60}{100} \times 100y = 60y$
=> Total selling price = $80y + 60y = 140y$ --------------------Eqn(2)
Comparing eqns(1) & (2), we get :
=> $210x = 140y$
=> $\frac{y}{x} = \frac{210}{140} = \frac{3}{2}$
$\therefore$ Required % = $\frac{3}{2} \times 100 = 150 \%$
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CCommunity
Solution
Let the cost price of each article = Rs. $100x$
=> C.P. of both articles = $2 \times 100x = 200x$
=> Selling price = $\frac{105}{100} \times 200x = 210x$ ------------------Eqn(1)
Let the marked price = Rs. $100y$
Selling price of 1st article after 20% discount = $\frac{80}{100} \times 100y = 80y$
Selling price of 2nd article after 40% discount = $\frac{60}{100} \times 100y = 60y$
=> Total selling price = $80y + 60y = 140y$ --------------------Eqn(2)
Comparing eqns(1) & (2), we get :
=> $210x = 140y$
=> $\frac{y}{x} = \frac{210}{140} = \frac{3}{2}$
$\therefore$ Required % = $\frac{3}{2} \times 100 = 150 \%$