Question

Imagine you have two large pitchers, A and B. A contains 10 litres of wine and B contains 10 litres of water. One litre of water is removed from B and poured into A. The liquid is mixed very well. Then one litre of the mixture from A is poured into B. Which of the following statements is true?

• A. The water contents in A is more than the wine contents in B
• B. The water contents in A is less than the wine contents in B
• C. The water contents in A is same as the wine contents in B
• D. None of these

Answer 1

The Correct Option is C

Initially, Pitcher A has 10 litres of wine, and Pitcher B has 10 litres of water. When 1 litre of water is transferred from B to A, the composition is:

• Pitcher A: 10L wine + 1L water = 11L mixture.
• Pitcher B: 9L water.

After mixing, 1 litre is removed from A and poured back into B. This 1 litre, consisting of 10/11 of wine and 1/11 of water (since the proportions are maintained), is transferred:

• Amount of wine in 1 litre = 10/11 L.
• Amount of water in 1 litre = 1/11 L.

By transferring this back to B, we calculate:

• Wine in B after transfer: 0 + 10/11 L = 10/11 L.
• Water in B after transfer: 9 + 1/11 L = 100/11 L.

Both pitchers return to 10 litres each. Thus:

• Water in A (initially 1L added) = 1 - 1/11 = 10/11 L.
• Wine in B = 10/11 L.

Hence, the water content in A is equal to the wine content in B, verifying the statement: The water contents in A is the same as the wine contents in B.