In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)

Options

A. a. 70%
B. b. 80%
C. c. 62%
D. d. 75%

Explanation

To solve the problem step by step, we need to find the percentage of water in the mixture after adding additional water.

### Step 1: Determine the initial amount of water in the mixture
Given that the proportion of water in the mixture is 75%, we can find the amount of water in the initial 60 gm mixture.

\[ \text{Initial amount of water} = 75\% \text{ of } 60 \text{ gm} = \frac{75}{100} \times 60 = 45 \text{ gm} \]

### Step 2: Calculate the amount of milk in the mixture
Since the total weight of the mixture is 60 gm and the amount of water is 45 gm, we can find the amount of milk.

\[ \text{Amount of milk} = \text{Total mixture} - \text{Amount of water} = 60 \text{ gm} - 45 \text{ gm} = 15 \text{ gm} \]

### Step 3: Add the additional water
Now, we add 15 gm of water to the mixture.

\[ \text{New amount of water} = \text{Initial water} + \text{Added water} = 45 \text{ gm} + 15 \text{ gm} = 60 \text{ gm} \]

### Step 4: Calculate the new total weight of the mixture
After adding 15 gm of water, the new total weight of the mixture becomes:

\[ \text{New total weight of mixture} = \text{Initial mixture} + \text{Added water} = 60 \text{ gm} + 15 \text{ gm} = 75 \text{ gm} \]

### Step 5: Calculate the percentage of water in the new mixture
Now we can find the percentage of water in the new mixture.

\[ \text{Percentage of water} = \left(\frac{\text{New amount of water}}{\text{New total weight of mixture}}\right) \times 100 = \left(\frac{60 \text{ gm}}{75 \text{ gm}}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage of water} = \frac{60}{75} \times 100 = 80\% \]

### Final Answer
The percentage of water in the new mixture is **80%**.

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