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Question

(A) Let the original quantity of the mixture be $x 	ext{ kg}$.Initially:Pure ghee $= 0.6x 	ext{ kg}$Vanaspati ghee $= 0.4x 	ext{ kg}$After adding $

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) Let the original quantity of the mixture be $x 	ext{ kg}$.Initially:Pure ghee $= 0.6x 	ext{ kg}$Vanaspati ghee $= 0.4x 	ext{ kg}$After adding $10 	ext{ kg}$ of pure ghee:New total quantity $= (x + 10) 	ext{ kg}$New quantity of vanaspati ghee remains $= 0.4x 	ext{ kg}$According to the problem, the new concentration of vanaspati is $20 \%$:$\frac{0.4x}{x + 10} = \frac{20}{100}$$\frac{0.4x}{x + 10} = \frac{1}{5}$Cross-multiplying:$5 	imes 0.4x = 1 	imes (x + 10)$$2x = x + 10$$x = 10 	ext{ kg}$Thus, the original quantity was $10 	ext{ kg}$.

In a certain quantity of ghee, $60 \%$ is pure ghee and $40 \%$ is vanaspati. If $10 \text{ kg}$ of pure ghee is added, the concentration of vanaspati ghee becomes $20 \%$. What was the original quantity (in $\text{ kg}$)?

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