In two alloys,gold and silver are in the rati | vedclass

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(D) In the first alloy of $10 	ext{ kg}$ with ratio $4:1$,the amount of gold is $\frac{4}{5} 	imes 10 = 8 	ext{ kg}$ and silver is $\frac{1}{5} 	i

Vedclass · Accepted Answer

$35$

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(D) In the first alloy of $10 	ext{ kg}$ with ratio $4:1$,the amount of gold is $\frac{4}{5} 	imes 10 = 8 	ext{ kg}$ and silver is $\frac{1}{5} 	imes 10 = 2 	ext{ kg}$.In the second alloy of $16 	ext{ kg}$ with ratio $1:3$,the amount of gold is $\frac{1}{4} 	imes 16 = 4 	ext{ kg}$ and silver is $\frac{3}{4} 	imes 16 = 12 	ext{ kg}$.Let the amount of pure gold added be $x 	ext{ kg}$.Total gold in the new alloy $= 8 + 4 + x = 12 + x 	ext{ kg}$.Total silver in the new alloy $= 2 + 12 = 14 	ext{ kg}$.The ratio of gold to silver in the new alloy is $3:2$,so $\frac{12 + x}{14} = \frac{3}{2}$.$2(12 + x) = 3 	imes 14 \Rightarrow 24 + 2x = 42 \Rightarrow 2x = 18 \Rightarrow x = 9 	ext{ kg}$.The total weight of the new alloy $= 10 + 16 + 9 = 35 	ext{ kg}$.

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