Question

Milk and water in two vessels A and B are in the ratios 4:3 and 2:3 respectively. In what ratio should the liquids from both vessels be mixed to obtain a new mixture (vessel C) that is half milk and half water?

• A. 1:1
• B. 7:5
• C. 2:4
• D. 1:3

Hint:

For mixture questions, convert ratios to fractions first, then use alligation: (A:B) $=\dfrac\textTarget-\textB\textA-\textTarget$. It avoids setting up simultaneous equations.

Answer 1

The Correct Option is B

Step 1: Express milk fractions in each vessel.
Vessel A: Milk:Water $=4:3 ⇒$ Milk fraction $=\dfrac{4}{4+3}=\dfrac{4}{7}$.
Vessel B: Milk:Water $=2:3 ⇒$ Milk fraction $=\dfrac{2}{2+3}=\dfrac{2}{5}$.
Step 2: Target mixture is half milk.
Required milk fraction in vessel C $=\dfrac{1}{2}$.
Step 3: Use alligation (or weighted average) to find the mixing ratio.
Ratio (A:B) $=\dfrac{\text{Target}-\text{B}}{\text{A}-\text{Target}}
=\dfrac{\dfrac{1}{2}-\dfrac{2}{5}}{\dfrac{4}{7}-\dfrac{1}{2}}
=\dfrac{\dfrac{1}{10}}{\dfrac{1}{14}}
=\dfrac{1}{10}\times\dfrac{14}{1}
=\dfrac{14}{10}
= \dfrac{7}{5}$.
⇒ Mix A:B $= 7:5$.
\[ \boxed{7:5} \]