CP of milk 80/- per litre. But seller sells milk at 70/- per litre with mixing water and got profit 40%. So, ratio of water to milk. (in solution)

We are given the following details:

- Cost Price (CP) of milk = ₹80 per litre
- Selling Price (SP) of the mixture = ₹70 per litre
- Profit = 40%

Let us solve the problem step by step to find the ratio of water to milk in the mixture.

### Step 1: Determine the actual Cost Price (CP) of the mixture
The seller is gaining a profit of 40%, which means:

\[
\text{Profit} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100
\]

Here, Profit is 40%, so:

\[
40 = \frac{70 - \text{CP of mixture}}{\text{CP of mixture}} \times 100
\]

Let \( x \) be the CP of the mixture. Now we solve for \( x \):

\[
40 = \frac{70 - x}{x} \times 100
\]

\[
0.40 = \frac{70 - x}{x}
\]

Multiply both sides by \( x \):

\[
0.40x = 70 - x
\]

Now, combine like terms:

\[
0.40x + x = 70
\]

\[
1.40x = 70
\]

Solve for \( x \):

\[
x = \frac{70}{1.40} = 50
\]

So, the cost price of the mixture is ₹50 per litre.

### Step 2: Apply the concept of mixing
In the mixture, water is mixed with milk. Water is free, so the cost of the mixture is solely based on the milk content.

Let the amount of milk in the mixture be \( M \) litres, and the total amount of the mixture be 1 litre. The cost price of milk is ₹80 per litre. Therefore, the total cost of the mixture can be expressed as:

\[
M \times 80 = 50
\]

Now solve for \( M \):

\[
M = \frac{50}{80} = 0.625
\]

So, the milk content in the mixture is 0.625 litres.

### Step 3: Calculate the water content
Since the total quantity of the mixture is 1 litre, the water content \( W \) is:

\[
W = 1 - M = 1 - 0.625 = 0.375 \, \text{litres}
\]

### Step 4: Find the ratio of water to milk
The ratio of water to milk is:

\[
\text{Water : Milk} = 0.375 : 0.625
\]

Simplifying the ratio by dividing both numbers by 0.125:

\[
\text{Water : Milk} = 3 : 5
\]

### Final Answer:
The ratio of water to milk is **3:5**.

---

Would you like further details or explanations on any part of the solution?

Here are 5 additional questions for practice:
1. If the selling price per litre was ₹75 instead of ₹70, what would the ratio of water to milk be?
2. What would the ratio be if the profit was only 20% instead of 40%?
3. How much water should be added to 10 litres of pure milk to achieve the same 40% profit?
4. What would the profit percentage be if no water was added and the milk was sold at ₹90 per litre?
5. How does the ratio of water to milk change if the cost price of milk changes to ₹100 per litre?

**Tip:** Whenever you're solving mixture problems, focus on the concept that water, being free, reduces the overall cost of the mixture.

Discover how to calculate the ratio of water to milk in a mixture where milk costs ₹80 per litre, but the seller sells the mixture at ₹70 per litre with a 40% profit. A detailed solution with steps covering profit and loss, mixture problems, and ratios. Perfect for students in Grades 8-10.

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