A dishonest milkman purchased milk at 10 per litre and mixed 5 litres of water in it. By selling the mixture at the rate of 10 per litre he earns a profit of 25%. The quantity of the amount of the mixture that he had was:

Options

A. 15 litres
B. 20 litres
C. 25 litres
D. 30 litres

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Cost Price of Milk
The milkman purchased milk at ₹10 per litre. If he has \( x \) litres of milk, the cost price (CP) of the milk is:
\[ \text{CP of milk} = 10x \text{ (in ₹)} \]

### Step 2: Calculate the Total Volume of the Mixture
The milkman mixes 5 litres of water with \( x \) litres of milk. Therefore, the total volume of the mixture is:
\[ \text{Total mixture} = x + 5 \text{ litres} \]

### Step 3: Determine the Selling Price of the Mixture
The milkman sells the mixture at ₹10 per litre. Thus, the selling price (SP) of the total mixture is:
\[ \text{SP} = 10 \times (x + 5) \text{ (in ₹)} \]

### Step 4: Calculate the Profit Percentage
The profit percentage is given as 25%. This means that the selling price is 125% of the cost price. Therefore, we can express this as:
\[ \text{SP} = \frac{125}{100} \times \text{CP} \]
Substituting the values we have:
\[ 10(x + 5) = \frac{125}{100} \times 10x \]

### Step 5: Simplify the Equation
We can simplify the equation:
\[ 10(x + 5) = 1.25 \times 10x \]
\[ 10x + 50 = 12.5x \]

### Step 6: Rearranging the Equation
Now, let's rearrange the equation to isolate \( x \):
\[ 50 = 12.5x - 10x \]
\[ 50 = 2.5x \]

### Step 7: Solve for \( x \)
Dividing both sides by 2.5 gives:
\[ x = \frac{50}{2.5} = 20 \text{ litres} \]

### Step 8: Calculate the Total Quantity of the Mixture
Now, we can find the total quantity of the mixture:
\[ \text{Total mixture} = x + 5 = 20 + 5 = 25 \text{ litres} \]

### Final Answer
Thus, the quantity of the mixture that the milkman had was **25 litres**.

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