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

Initially:

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

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

Now we need to calculate how much milk and water are in that 150 cc mixture:

• Total in cup: 150 cc milk + 500 cc water = 650 cc
• Fraction of milk: \( \frac{150}{650} = \frac{3}{13} \)
• Fraction of water: \( \frac{500}{650} = \frac{10}{13} \)

So the 150 cc taken back to the glass contains:

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

After the second transfer:

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

Step 3: Final Ratio of Milk in Glass to Water in Cup

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

Final Answer:

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

Answer 2

You are given:

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

Two transfers are made:

1. 150 cc of milk is transferred from the glass to the cup
2. 150 cc of the resulting mixture in the cup is transferred back to the glass

What is the final ratio of water in the glass to milk in the cup?

Step 1: Transfer 150 cc of Milk to the Cup

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

Step 2: Transfer 150 cc of Mixture Back to the Glass

Mixture in cup is 150 cc milk and 500 cc water → ratio \( 3:10 \).
So in 150 cc of this mixture:

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

After Transfer:

• Glass:
  • Milk = \( 350 + 34.62 = 384.62 \) cc
  • Water = \( 0 + 115.38 = 115.38 \) cc
• Cup:
  • Milk = \( 150 - 34.62 = 115.38 \) cc
  • Water = \( 500 - 115.38 = 384.62 \) cc

Step 3: Find Final Ratio

Water in glass : Milk in cup \[ = 115.38 : 115.38 = \boxed{1 : 1} \]

Final Answer:

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