In an alloy, zinc and copper are in the ratio 1 : 2. In the second alloy, the same elements are in the ratio 2 : 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloys is –

A. 3 : 10 B. 3 : 7 C. 10 : 3 D. 7 : 3 Answer: Option A
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Solution(By Apex Team)

You must know that we can apply this rule over the fractional value of either zinc or copper. Let us consider the fractional value of zinc.
Therefore, they should be mixed in the ratio $\begin{aligned}&=\frac{1}{65}:\frac{2}{39}\\ &\text{ or },\frac{1}{65}\times\frac{39}{2}\\ &=\frac{3}{10}\\ &\text{ or, }3:10\end{aligned}$
Alternate: Let them be mixed in the ratio x : y Then, in 1st alloy, Zinc = $\Large\frac{x}{3}$ and Copper $\Large\frac{2x}{3}$ 2nd alloy, Zinc = $\Large\frac{2 y}{5}$ and Copper $\Large\frac{3 y}{5}$ Now, we have; $\begin{aligned}&\frac{x}{3}+\frac{2y}{5}:\frac{2x}{3}+\frac{3y}{5}=5:8\\ &\text{ or },\frac{5x+6y}{10x+9y}=\frac{5}{8}\\ &\text{ or },40x+48y=50x+45y\\ &\text{ or },10x=3y\\ &\therefore\frac{x}{y}=\frac{3}{10}\end{aligned}$ Thus, the required ratio = 3 : 10

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