A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc 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:
Question:
A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc 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 glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc 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:
Options
Answer: 1:1
Explanation:
Step 1: Initial amounts Glass: 500 cc milk, 0 water Cup: 0 milk, 500 cc water Step 2: First transfer (150 cc milk → cup) Milk transferred from glass to cup = 150 cc Glass now: 500 - 150 = 350 cc milk, 0 water Cup now: 500 water + 150 milk = 650 cc total Fraction of milk in cup = 150/650 = 3/13 Fraction of water in cup = 500/650 = 10/13 Step 3: Second transfer (150 cc mixture → glass) 150 cc mixture is taken from cup → 150 × (3/13) = 450/13 ≈ 34.615 cc milk 150 × (10/13) = 1500/13 ≈ 115.385 cc water This 150 cc is added to glass: Glass milk: 350 + 450/13 = 350 + 34.615 ≈ 384.615 cc Glass water: 0 + 115.385 cc ≈ 115.385 cc Step 4: Amounts in cup after second transfer Cup milk: 150 - 34.615 ≈ 115.385 cc Cup water: 500 - 115.385 ≈ 384.615 cc Step 5: Ratio Water in glass : milk in cup = 115.385 : 115.385 = 1 : 1
Explanation:
Step 1: Initial amounts Glass: 500 cc milk, 0 water Cup: 0 milk, 500 cc water Step 2: First transfer (150 cc milk → cup) Milk transferred from glass to cup = 150 cc Glass now: 500 - 150 = 350 cc milk, 0 water Cup now: 500 water + 150 milk = 650 cc total Fraction of milk in cup = 150/650 = 3/13 Fraction of water in cup = 500/650 = 10/13 Step 3: Second transfer (150 cc mixture → glass) 150 cc mixture is taken from cup → 150 × (3/13) = 450/13 ≈ 34.615 cc milk 150 × (10/13) = 1500/13 ≈ 115.385 cc water This 150 cc is added to glass: Glass milk: 350 + 450/13 = 350 + 34.615 ≈ 384.615 cc Glass water: 0 + 115.385 cc ≈ 115.385 cc Step 4: Amounts in cup after second transfer Cup milk: 150 - 34.615 ≈ 115.385 cc Cup water: 500 - 115.385 ≈ 384.615 cc Step 5: Ratio Water in glass : milk in cup = 115.385 : 115.385 = 1 : 1
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