Question

A glass contains 500cc of milk and a cup contains 500cc of water.From the glass,150cc of milk is transferred to the cup and mixed thoroughly. Next,150cc of this mixture is transferred from the cup to the glass.Now,the amount of water in the glass and the amount of milk in the cup are in the ratio

• A. \(3\ratio10\)
• B. \(10\ratio3\)
• C. \(1\ratio1\)
• D. \(10\ratio13\)

Answer 1

The Correct Option is C

Initial state:

• Glass: 500 cc milk, 0 cc water
• Cup: 0 cc milk, 500 cc water

Step 1: Transfer 150 cc of milk from glass to cup

• Glass: \(500 - 150 = 350\) cc milk
• Cup: 150 cc milk + 500 cc water = 650 cc total volume

Step 2: Transfer 150 cc of mixture from cup back to glass

Calculate milk and water amounts in the 150 cc mixture:

• Total in cup: 650 cc
• Milk proportion: \( \frac{150}{650} = \frac{3}{13} \)
• Water proportion: \( \frac{500}{650} = \frac{10}{13} \)

Amount transferred back to glass:

• Milk: \( \frac{3}{13} \times 150 \approx 34.62 \) cc
• Water: \( \frac{10}{13} \times 150 \approx 115.38 \) cc

Contents after Step 2:

• Glass: \(350 + 34.62 \approx 384.62\) cc milk, \(0 + 115.38 \approx 115.38\) cc water
• Cup: \(150 - 34.62 \approx 115.38\) cc milk, \(500 - 115.38 \approx 384.62\) cc water

Step 3: Determine final ratio of milk in glass to water in cup

\[ \text{Milk in Glass} : \text{Water in Cup} \approx 384.62 : 384.62 = \boxed{1 : 1} \]

Final Answer:

\[ \boxed{\text{Option (C): } 1 : 1} \]