Question : Two mixtures A and B have the following compositions:
Mixture A has copper and tin in a ratio of 1 : 2
Mixture B has copper and tin in a ratio of 1 : 3
If equal quantities of mixtures A and B are used for producing mixture C, then find the ratio of copper and tin in mixture C.
Option 1: 2 : 5
Option 2: 1 : 5
Option 3: 7 : 17
Option 4: 7 : 12
Correct Answer: 7 : 17
Solution :
Assume that the quantities of copper and tin in mixtures A and B are such that the total quantity of each metal is x units copper and y units tin.
Mixture A:
Copper = $\frac{x}{3}$ unit
Tin = $\frac{2x}{3}$ unit
Mixture B:
Copper = $\frac{x}{4}$ unit
Tin = $\frac{3x}{4}$ unit
Now, if equal quantities of A and B are mixed to form C, we can add the corresponding quantities of copper and tin and can add total tin and total copper.
Mixture C:
Copper = ($\frac{x}{3}$ unit + $\frac{x}{4}$ unit) = $\frac{7x}{12}$ unit
Tin = ($\frac{2x}{3}$ unit +$\frac{3x}{4}$ unit) = $\frac{17x}{12}$ unit
So, the ratio of copper to tin in mixture C $=\frac{\frac{7x}{12}}{\frac{17x}{12}}=\frac{7}{17}$
Hence, the correct answer is 7 : 17.
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