• # question_answer 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. In what ratio should these two alloys be mixed to form a new alloy in which the two elements are in ratio 5 : 8? A)  10 : 3   B)         3 : 10   C)         3 : 7    D)         2 : 7

Solution :

Let them be mixed in the ratio $x:y$. Then, in 1st alloy, zinc $=\frac{x}{3}$ and copper $=\frac{2x}{3}$ 2nd alloy, zinc $=\frac{2y}{5}$ and copper $=\frac{3y}{5}$ Now, we have, $\frac{x}{3}+\frac{2y}{5}:\frac{2x}{3}+\frac{3y}{5}=5:8$ $\Rightarrow$   $\frac{5x+6y}{10x+9y}=\frac{5}{8}$ $\Rightarrow$   $40x+48y=50x+45y$ $\Rightarrow$   $10x=3y$ $\Rightarrow$   $\frac{x}{y}=\frac{3}{10}$ $\therefore$      Required ratio = 3 : 10 Alternatively Let us consider the fractional value of zinc Therefore, they should be mixed in the ratio.   $\frac{1}{65}:\frac{2}{39}$ $\Rightarrow$               $\frac{1}{65}\times \frac{39}{2}=\frac{3}{10}=3:10$

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