A dishonest milkman buy 40 lt milk at Rs. 193/lt and mixed some water to this milk and then sold it Rs. 193 /lt and gains 25 % profit. Find the quantity of water that he mixed.

Answer

To solve the problem step-by-step, we will follow the reasoning laid out in the video transcript. Here’s the structured solution:

### Step 1: Understand the Problem
A dishonest milkman buys 40 liters of milk at Rs. 193 per liter and mixes some water with it. He sells the mixture at Rs. 193 per liter and gains a 25% profit. We need to find out how much water he mixed.

### Step 2: Define Variables
Let the quantity of water mixed be \( x \) liters.

### Step 3: Calculate the Total Quantity of Mixture
The total quantity of the mixture (milk + water) is:
\[ \text{Total mixture} = 40 \text{ liters (milk)} + x \text{ liters (water)} = 40 + x \text{ liters} \]

### Step 4: Calculate the Cost Price of Milk
The cost price of 40 liters of milk is:
\[ \text{Cost Price (CP)} = 40 \text{ liters} \times 193 \text{ Rs/liter} = 7720 \text{ Rs} \]
Since water is free, the total cost price of the mixture remains Rs. 7720.

### Step 5: Calculate the Selling Price of the Mixture
The selling price of the mixture is:
\[ \text{Selling Price (SP)} = \text{Selling Price per liter} \times \text{Total quantity sold} = 193 \text{ Rs/liter} \times (40 + x) \text{ liters} \]
\[ \text{SP} = 193(40 + x) \text{ Rs} \]

### Step 6: Use the Profit Percentage to Set Up an Equation
We know the profit percentage is given as 25%. The formula for profit percentage is:
\[ \text{Profit Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]
Substituting the known values:
\[ 25 = \frac{193(40 + x) - 7720}{7720} \times 100 \]

### Step 7: Simplify the Equation
First, divide both sides by 100:
\[ 0.25 = \frac{193(40 + x) - 7720}{7720} \]
Now, multiply both sides by 7720:
\[ 0.25 \times 7720 = 193(40 + x) - 7720 \]
Calculating \( 0.25 \times 7720 \):
\[ 1930 = 193(40 + x) - 7720 \]
Rearranging gives:
\[ 193(40 + x) = 1930 + 7720 \]
\[ 193(40 + x) = 9650 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 193:
\[ 40 + x = \frac{9650}{193} \]
Calculating \( \frac{9650}{193} \):
\[ 40 + x = 50 \]
Subtracting 40 from both sides:
\[ x = 10 \text{ liters} \]

### Conclusion
The quantity of water mixed by the milkman is **10 liters**.

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