In what proportion water be mixed with spirit to gain `12.5%` by selling it at cost price?

Options

A. 3:5
B. 1:8
C. 2:7
D. 1:9

Answer

To solve the problem of mixing water with spirit to achieve a profit of 12.5% while selling at the cost price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Profit Percentage**:
We want to achieve a profit of 12.5%. This means that if we sell the mixture at the cost price, we need to find out how much water we need to mix with the spirit to achieve this profit.

2. **Convert Percentage to Fraction**:
The profit percentage of 12.5% can be converted to a fraction.
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]

3. **Identify the Components**:
In this scenario, we can think of the components as follows:
- The spirit represents the higher value component.
- The water represents the lower value component (which is essentially zero cost).

4. **Set Up the Ratio**:
According to the fraction we derived, \(\frac{1}{8}\), we can interpret this as:
- 1 part of water (the lower value component)
- 8 parts of spirit (the higher value component)

5. **Write the Proportion**:
Therefore, the proportion of water to spirit can be expressed as:
\[ \text{Water : Spirit} = 1 : 8 \]

### Final Answer:
Water should be mixed with spirit in the ratio of **1:8**.

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