A man sold a watch at Rs. 6000, at a loss of `33 1/3%` . Find the cost price ?

Answer

To find the cost price of the watch sold at a loss of 33 1/3%, we can follow these steps:

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 6000
- Loss Percentage (LP) = 33 1/3% = 33.33%

### Step 2: Convert the loss percentage into a fraction
33 1/3% can be expressed as:
\[ \text{Loss Percentage} = \frac{33 \times 3 + 1}{3} = \frac{100}{3} \]
Thus, the loss percentage is \( \frac{100}{3} \% \).

### Step 3: Use the formula to find the Cost Price (CP)
The formula to find the Cost Price when there is a loss is:
\[ CP = \frac{SP \times 100}{100 - LP} \]
Substituting the values we have:
\[ CP = \frac{6000 \times 100}{100 - \frac{100}{3}} \]

### Step 4: Simplify the denominator
First, calculate \( 100 - \frac{100}{3} \):
\[ 100 = \frac{300}{3} \quad \text{(to have a common denominator)} \]
So,
\[ 100 - \frac{100}{3} = \frac{300}{3} - \frac{100}{3} = \frac{200}{3} \]

### Step 5: Substitute back into the formula
Now substitute back into the formula:
\[ CP = \frac{6000 \times 100}{\frac{200}{3}} \]

### Step 6: Simplify the expression
To simplify:
\[ CP = 6000 \times 100 \times \frac{3}{200} \]
\[ = \frac{6000 \times 300}{200} \]
\[ = \frac{1800000}{200} \]
\[ = 9000 \]

### Conclusion
The Cost Price (CP) of the watch is Rs. 9000.

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