Question

The ratio of alcohol to water in two containers, A and B, is 5:3 and 1:3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litres of liquid, which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?

• A. 1.4
• B. 1.05
• C. 0.35
• D. 1.1

Hint:

The Alligation ratio \( (x-m)/(m-y) \) represents the ratio of quantities of the two sources.

Answer 1

The Correct Option is A

Step 1: Find each mixture's alcohol fraction.
Container A is alcohol to water 5:3, so its alcohol fraction is $\dfrac{5}{8}$. Container B is 1:3, so its alcohol fraction is $\dfrac{1}{4}$. The target blend must be half alcohol, fraction $\dfrac{1}{2}$.
Step 2: Set up the unknown amounts.
Let $a$ litres come from A and $b$ litres from B, with $a + b = 2.1$ litres of final liquid.
Step 3: Write the alcohol balance.
Total alcohol must be half of 2.1, namely 1.05 litres: $\dfrac{5}{8}a + \dfrac{1}{4}b = 1.05$.
Step 4: Substitute $b = 2.1 - a$.
$\dfrac{5}{8}a + \dfrac{1}{4}(2.1 - a) = 1.05$. This gives $\dfrac{5}{8}a + 0.525 - 0.25a = 1.05$.
Step 5: Solve for $a$.
$\left(0.625 - 0.25\right)a = 1.05 - 0.525$, so $0.375a = 0.525$ and $a = \dfrac{0.525}{0.375} = 1.4$.
Step 6: Verify the mix.
Then $b = 2.1 - 1.4 = 0.7$. Alcohol $= \dfrac{5}{8}(1.4) + \dfrac{1}{4}(0.7) = 0.875 + 0.175 = 1.05$, exactly half. So draw 1.4 litres from A, matching option 1.
\[ \boxed{1.4} \]