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                

Correct Answer: B

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.   \[\frac{1}{65}:\frac{2}{39}\] \[\Rightarrow \]               \[\frac{1}{65}\times \frac{39}{2}=\frac{3}{10}=3:10\]