A shopkeeper sells 25 articles at Rs. 45 per | vedclass

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(D) Given,selling price $(S.P.)$ after $10 \%$ discount $= Rs. 45$.Let the marked price be $M.P.$. Since $10 \%$ discount is given,$S.P. = M.P. 	imes

Vedclass · Accepted Answer

$66 \frac{2}{3}$

Vedclass · Answer

(D) Given,selling price $(S.P.)$ after $10 \%$ discount $= Rs. 45$.Let the marked price be $M.P.$. Since $10 \%$ discount is given,$S.P. = M.P. 	imes (1 - 0.10) = 0.9 	imes M.P.$$45 = 0.9 	imes M.P. \implies M.P. = \frac{45}{0.9} = Rs. 50$.If no discount is given,the new selling price $(S.P._{new})$ will be equal to the marked price,so $S.P._{new} = Rs. 50$.Now,the shopkeeper earns a $50 \%$ profit on the original $S.P.$ of $Rs. 45$.Cost price $(C.P.)$ $= \frac{S.P.}{1 + 	ext{profit } \%} = \frac{45}{1 + 0.50} = \frac{45}{1.5} = Rs. 30$.If no discount is given,the profit percentage is calculated as:$	ext{Profit } \% = \frac{S.P._{new} - C.P.}{C.P.} 	imes 100$$	ext{Profit } \% = \frac{50 - 30}{30} 	imes 100 = \frac{20}{30} 	imes 100 = \frac{2}{3} 	imes 100 = 66 \frac{2}{3} \%$.

$A$ shopkeeper sells $25$ articles at $Rs. 45$ per article after giving a $10 \%$ discount and earns a $50 \%$ profit. If no discount is given,the profit percentage gained is......$\%$

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