A shopkeeper has to sell 24 text{ kg} of suga | vedclass

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(B) Let the quantity of sugar sold at a loss be $x 	ext{ kg}$.Then,the quantity of sugar sold at a gain is $(24 - x) 	ext{ kg}$.Let the cost price $

Vedclass · Accepted Answer

$9.6$

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(B) Let the quantity of sugar sold at a loss be $x 	ext{ kg}$.Then,the quantity of sugar sold at a gain is $(24 - x) 	ext{ kg}$.Let the cost price $(CP)$ per $	ext{kg}$ be $Rs. 1$.Total $CP = 24 	imes 1 = Rs. 24$.Total profit required is $10 \%$,so total selling price $(SP)$ = $110 \% 	ext{ of } 24 = 1.1 	imes 24 = Rs. 26.4$.Selling price of the part sold at $20 \% 	ext{ gain} = (24 - x) 	imes 1.20$.Selling price of the part sold at $5 \% 	ext{ loss} = x 	imes 0.95$.Equating the total $SP$: $1.20(24 - x) + 0.95x = 26.4$.$28.8 - 1.20x + 0.95x = 26.4$.$28.8 - 0.25x = 26.4$.$0.25x = 28.8 - 26.4 = 2.4$.$x = \frac{2.4}{0.25} = 9.6 	ext{ kg}$.

$A$ shopkeeper has to sell $24 \text{ kg}$ of sugar. He sells a part of these at a gain of $20 \%$ and the rest at a loss of $5 \%$. If on the whole he earns a profit of $10 \%$,what is the quantity of sugar (in $\text{kg}$) sold at a loss?

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