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

Options

A. 20%
B. 40%
C. 50%
D. 60%

Answer

To find the profit percentage at Cost Price (C.P.) when given a profit percentage at Selling Price (S.P.), we can follow these steps:

### Step 1: Understand the given profit percentage
The profit percentage given is \( 33 \frac{1}{3} \% \). This can be converted into a fraction.
\[ 33 \frac{1}{3} \% = \frac{100}{3} \% \]

### Step 2: Assume a Selling Price (S.P.)
Let’s assume the Selling Price (S.P.) is \( X \).

### Step 3: Calculate the profit in terms of S.P.
The profit at Selling Price can be calculated using the formula:
\[ \text{Profit} = \left( \frac{100}{3} \% \text{ of } X \right) = \frac{100}{3} \times \frac{X}{100} = \frac{X}{3} \]

### Step 4: Calculate the Cost Price (C.P.)
The Cost Price (C.P.) can be calculated as:
\[ \text{C.P.} = \text{S.P.} - \text{Profit} \]
Substituting the values we have:
\[ \text{C.P.} = X - \frac{X}{3} \]
To simplify this, we can express \( X \) as \( \frac{3X}{3} \):
\[ \text{C.P.} = \frac{3X}{3} - \frac{X}{3} = \frac{2X}{3} \]

### Step 5: Calculate the profit percentage at C.P.
Now, we need to find the profit percentage at C.P. using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{C.P.}} \right) \times 100 \]
Substituting the profit and C.P. values:
\[ \text{Profit Percentage} = \left( \frac{\frac{X}{3}}{\frac{2X}{3}} \right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Conclusion
Thus, the profit percentage at Cost Price (C.P.) is \( 50\% \).