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

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Accepted Answer

1. **Initial Setup:**  
   - Glass: 500 cc milk, 0 cc water.  
   - Cup: 0 cc milk, 500 cc water.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743575828/aptidude_questions/rdbuqlgerylaaqgtyyzw.png)

2. **First Transfer (150 cc milk from Glass to Cup):**  
   - Glass: $$500 - 150 = 350$$ cc milk, $$0$$ cc water.  
   - Cup: $$150$$ cc milk, $$500$$ cc water (total $$650$$ cc mixture).

3. **Second Transfer (150 cc mixture from Cup to Glass):**  
   - The ratio of milk to water in the cup is $$150 : 500 = 3 : 10$$.  
   - From the $$150$$ cc mixture transferred:  
     - Milk = $$\frac{3}{13} 	imes 150 = \frac{450}{13}$$ cc.  
     - Water = $$\frac{10}{13} 	imes 150 = \frac{1500}{13}$$ cc.

- **Glass after transfer:**  
     - Milk = $$350 + \frac{450}{13} = \frac{4900}{13}$$ cc.  
     - Water = $$\frac{1500}{13}$$ cc.

- **Cup after transfer:**  
     - Milk = $$150 - \frac{450}{13} = \frac{1500}{13}$$ cc.  
     - Water = $$500 - \frac{1500}{13} = \frac{5000}{13}$$ cc.

4. **Final Observation:**  
   - In the glass: Water = $$\frac{1500}{13}$$.  
   - In the cup: Milk = $$\frac{1500}{13}$$.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743575834/aptidude_questions/s6wjbtia8ihls8fgjshs.png)

The amounts of water in the glass and milk in the cup are equal, resulting in a ratio of **1 : 1**.

Thus, the correct answer is **C. 1 : 1**.

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