In a mixture of milk and water, the proportion of milk by weight is 60%. If from the 80 gm mixture, 20 gm of mixture is taken out and 6 gm of pure water is added: to the mixture then find the ratio of milk and water in the new mixture.

Options

A. `5:6 `
B. `6:5 `
C. `4:3`
D. `3:2 `

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the initial quantities of milk and water in the mixture.
Given that the mixture is 60% milk, we can calculate the amount of milk in the 80 gm mixture.

- **Milk in the mixture** = 60% of 80 gm
\[ \text{Milk} = \frac{60}{100} \times 80 = 48 \text{ gm} \]

- **Water in the mixture** = Total mixture - Milk
\[ \text{Water} = 80 \text{ gm} - 48 \text{ gm} = 32 \text{ gm} \]

### Step 2: Calculate the quantities of milk and water after removing 20 gm of the mixture.
When 20 gm of the mixture is taken out, we need to find out how much milk and water is in that 20 gm.

- **Milk in 20 gm of mixture** = (Milk in 80 gm) × (20 gm / 80 gm)
\[ \text{Milk in 20 gm} = \frac{48 \text{ gm}}{80 \text{ gm}} \times 20 \text{ gm} = 12 \text{ gm} \]

- **Water in 20 gm of mixture** = (Water in 80 gm) × (20 gm / 80 gm)
\[ \text{Water in 20 gm} = \frac{32 \text{ gm}}{80 \text{ gm}} \times 20 \text{ gm} = 8 \text{ gm} \]

Now, subtract these quantities from the original amounts:

- **Remaining Milk** = Initial Milk - Milk removed
\[ \text{Remaining Milk} = 48 \text{ gm} - 12 \text{ gm} = 36 \text{ gm} \]

- **Remaining Water** = Initial Water - Water removed
\[ \text{Remaining Water} = 32 \text{ gm} - 8 \text{ gm} = 24 \text{ gm} \]

### Step 3: Add 6 gm of pure water to the remaining mixture.
Now, we add 6 gm of pure water to the remaining water:

- **New Water Quantity** = Remaining Water + Added Water
\[ \text{New Water} = 24 \text{ gm} + 6 \text{ gm} = 30 \text{ gm} \]

### Step 4: Calculate the final ratio of milk to water in the new mixture.
Now we have:

- **Final Milk** = 36 gm
- **Final Water** = 30 gm

The ratio of milk to water is:

\[ \text{Ratio} = \frac{\text{Milk}}{\text{Water}} = \frac{36}{30} = \frac{6}{5} \]

### Final Answer:
The ratio of milk to water in the new mixture is **6:5**.

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