A trader allows a trade discount of 20 % and | vedclass

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Question

(C) Let the $C.P.$ (Cost Price) of the article be $₹ 100$ and the marked price be $₹ x$.The trade discount is $20 \%$ and the cash discount is $6 \fra

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) Let the $C.P.$ (Cost Price) of the article be $₹ 100$ and the marked price be $₹ x$.The trade discount is $20 \%$ and the cash discount is $6 \frac{1}{4} \% = 6.25 \%$.The single equivalent discount is calculated as:$D = \left( d_1 + d_2 - \frac{d_1 	imes d_2}{100} ight) \% = \left( 20 + 6.25 - \frac{20 	imes 6.25}{100} ight) \% = (26.25 - 1.25) \% = 25 \%$.Selling Price $(S.P.)$ after discount $= x 	imes (100 - 25) \% = x 	imes 0.75$.Given that the trader gets a net gain of $20 \%$,so $S.P. = C.P. + 20 \% 	ext{ of } C.P. = 100 + 20 = ₹ 120$.Equating the two expressions for $S.P.$:$x 	imes 0.75 = 120$$x = \frac{120}{0.75} = \frac{12000}{75} = 160$.The marked price is $₹ 160$,which is $60 \%$ above the cost price of $₹ 100$.

$A$ trader allows a trade discount of $20 \%$ and a cash discount of $6 \frac{1}{4} \%$ on the marked price of the goods and gets a net gain of $20 \%$ of the cost. By how much above the cost should the goods be marked for the sale? (in $\%$)

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