A person calculates `33(1)/(3)%` loss at S.P. find his loss at C.P.

Answer

To solve the problem step by step, we will first convert the loss percentage into a fraction and then find the loss at the cost price (C.P.) based on the selling price (S.P.).

### Step-by-step Solution:

1. **Convert the Loss Percentage to a Fraction:**
The loss percentage given is \(33 \frac{1}{3}\%\).
- Convert \(33 \frac{1}{3}\%\) into an improper fraction:
\[ 33 \frac{1}{3} = \frac{100}{3}\% \]

2. **Express the Loss in Terms of Selling Price (S.P.):**
- Since the loss percentage is calculated on the selling price (S.P.), we can express the loss (L) as:
\[ L = \frac{100}{3} \times \frac{S.P.}{100} = \frac{1}{3} \times S.P. \]

3. **Assume a Value for Selling Price (S.P.):**
- For simplicity, let's assume \(S.P. = 3\) (you can choose any value, but 3 makes calculations easier).
- Then, the loss would be:
\[ L = \frac{1}{3} \times 3 = 1. \]

4. **Calculate the Cost Price (C.P.):**
- The relationship between C.P., S.P., and loss is given by:
\[ C.P. = S.P. + L. \]
- Substituting the values we have:
\[ C.P. = 3 + 1 = 4. \]

5. **Calculate the Loss Percentage at Cost Price (C.P.):**
- The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{L}{C.P.}\right) \times 100. \]
- Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{1}{4}\right) \times 100 = 25\%. \]

### Final Answer:
The loss percentage at Cost Price (C.P.) is **25%**.

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