A person has a chemical of 25 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at 20/litre he may get a profit of 25%?

Options

A. 14:9
B. 15:8
C. 16:9
D. 17:7

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step-by-Step Solution:

1. **Identify the Cost Price (CP) of the Chemical**:
The cost price of the chemical is given as ₹25 per litre.

2. **Determine the Selling Price (SP) and Profit Percentage**:
The selling price of the mixture is ₹20 per litre, and the desired profit is 25%.

3. **Calculate the Cost Price of the Mixture**:
To find the cost price of the mixture that allows for a 25% profit when sold at ₹20, we use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Since profit is 25% of CP, we can express it as:
\[ \text{SP} = \text{CP} + 0.25 \times \text{CP} = 1.25 \times \text{CP} \]
Rearranging gives:
\[ \text{CP} = \frac{\text{SP}}{1.25} \]
Substituting the selling price:
\[ \text{CP} = \frac{20}{1.25} = 16 \]

4. **Set Up the Allegation Method**:
Now we have:
- CP of the chemical = ₹25
- CP of water = ₹0 (since water is free)
- CP of the mixture = ₹16

We can set up the allegation:
\[ \text{CP of Chemical} \quad \text{CP of Mixture} \quad \text{CP of Water} \]
\[ 25 \quad \quad 16 \quad \quad 0 \]

5. **Calculate the Differences**:
- Difference between the CP of the chemical and the CP of the mixture:
\[ 25 - 16 = 9 \]
- Difference between the CP of water and the CP of the mixture:
\[ 16 - 0 = 16 \]

6. **Determine the Ratio**:
The ratio of the quantity of chemical to the quantity of water is given by the differences calculated:
\[ \text{Ratio} = 9 : 16 \]

### Final Answer:
The ratio in which water should be mixed with the chemical is **9:16**.

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