Question : Two alloys consist of copper and tin. The copper-to-tin ratio in the first alloy is 1 : 3, and in the second alloy, it is 2 : 5. What ratio should the two alloys be mixed in to create a new alloy with a tin-to-copper ratio of 8 : 3?
Option 1: 3 : 5
Option 2: 4 : 7
Option 3: 3 : 8
Option 4: 5 : 11
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Correct Answer: 4 : 7
Solution :
Given: The ratio of copper and tin in the first alloy is 1 : 3.
And in the second alloy is 2 : 5.
Let the alloys be mixed in the ratio of $x:y$.
Copper in first alloy = $\frac{x}{4}$
Tin in first alloy = $\frac{3x}{4}$
Copper in second alloy = $\frac{2y}{7}$
Tin in second alloy = $\frac{5y}{7}$
As per the given condition:
$(\frac{x}{4}+\frac{2y}{7}):(\frac{3x}{4}+\frac{5y}{7})=\frac{3}{8}$
⇒ $(\frac{7x+8y}{28}):(\frac{21x+20y}{28})=\frac{3}{8}$
⇒ $56x+64y=63x+60y$
⇒ $4y=7x$
$\therefore x:y=4:7$
Hence, the correct answer is 4 : 7.
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