Question

Three containers have their volumes in the ratio \(3:4:5\). They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of \((4:1), (3:1)\) and \((5:2)\) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is

• A. \(89:71\)
• B. \(191:72\)
• C. \(157:71\)
• D. \(157:53\)
• E. \(151:48\)

Answer 1

The Correct Option is D

Concept: Use
weighted average of ratios:

• Convert each mixture into actual milk and water
• Multiply by container volumes

Step 1: Assume volumes.
\[ 3, 4, 5 \]
Step 2: Find milk and water.
Container 1: \[ \text{Milk} = \frac{4}{5} \times 3 = \frac{12}{5}, \quad \text{Water} = \frac{1}{5} \times 3 = \frac{3}{5} \] Container 2: \[ \text{Milk} = \frac{3}{4} \times 4 = 3, \quad \text{Water} = \frac{1}{4} \times 4 = 1 \] Container 3: \[ \text{Milk} = \frac{5}{7} \times 5 = \frac{25}{7}, \quad \text{Water} = \frac{2}{7} \times 5 = \frac{10}{7} \]
Step 3: Add all.
Milk: \[ \frac{12}{5} + 3 + \frac{25}{7} = \frac{84 + 105 + 125}{35} = \frac{314}{35} \] Water: \[ \frac{3}{5} + 1 + \frac{10}{7} = \frac{21 + 35 + 50}{35} = \frac{106}{35} \]
Step 4: Final ratio.
\[ \frac{314}{35} : \frac{106}{35} = 314 : 106 = 157 : 53 \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Incorrect $\times$
• (D) Correct \checkmark
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (D).