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. 3:10
• B. 2:1
• C. 1:1
• D. 1:2

Answer 1

The Correct Option is C

After transferring 150 cc of milk to the cup, the cup contains 150 cc of milk and 500 cc of water. The total mixture in the cup is now 650 cc.
150 cc of the mixture is transferred back to the glass. The amount of milk in this 150 cc mixture is:
\[ \frac{150}{650} \times 150 = 34.615 \, \text{cc of milk} \]
The remaining amount of water in the cup is:
\[ 150 - 34.615 = 115.385 \, \text{cc of water} \]
The amount of water in the glass is now:
\[ 500 - 115.385 = 384.615 \, \text{cc of water} \]
The amount of milk in the cup is 34.615 cc. Therefore, the ratio of water in the glass to milk in the cup is:
\[ \frac{384.615}{34.615} = 1:1 \]

When transferring mixtures, calculate the proportions of each substance in the mixture and apply them accordingly.