Question

Two equal glasses filled with mixtures of alcohol and water in the proportions of \(2:1\) and \(1:1\) respectively were emptied into a third glass. What is the proportion of alcohol and water in the third glass?

• A. 5 : 7
• B. 7 : 5
• C. 7 : 6
• D. 6 : 7

Hint:

When mixing two solutions of equal volume, simply take the average contribution of each component. Always assume an easy number like 100 or 300 ml for quick calculations.

Answer 1

The Correct Option is B

Step 1: Assume equal quantities
Let each glass contain \(300\) ml (for easy calculation).
Step 2: First glass (ratio \(2:1\))
Alcohol \(=\frac{2}{3}\times 300=200\) ml, Water \(=100\) ml.
Step 3: Second glass (ratio \(1:1\))
Alcohol \(=\frac{1}{2}\times 300=150\) ml, Water \(=150\) ml.
Step 4: Combine into third glass
Total Alcohol \(=200+150=350\) ml.
Total Water \(=100+150=250\) ml.
Step 5: Simplify ratio
Alcohol : Water \(=350:250=7:5\).
\[ \boxed{7:5} \]