Find the cost price of article which is sold at Rs 70150 at a loss of 23.33%

Options

A. Rs 91500
B. Rs 90000
C. Rs 90500
D. Rs 94650

Answer

To find the cost price of an article sold at Rs. 70,150 with a loss of 23.33%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss Percentage
The formula to calculate the Selling Price when there is a loss is:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]

### Step 2: Identify the values given in the problem
- Selling Price (SP) = Rs. 70,150
- Loss Percentage = 23.33%

### Step 3: Convert the loss percentage into a decimal
To use the formula, we need to convert the loss percentage into a decimal:
\[ Loss\% = 23.33\% = \frac{23.33}{100} = 0.2333 \]

### Step 4: Calculate the percentage of Cost Price that corresponds to the Selling Price
Since there is a loss of 23.33%, the percentage of the Cost Price that corresponds to the Selling Price is:
\[ 100\% - 23.33\% = 76.67\% \]

### Step 5: Set up the equation using the Selling Price and the percentage of Cost Price
Using the Selling Price and the percentage of Cost Price:
\[ SP = CP \times \left( \frac{76.67}{100} \right) \]
Substituting the values we have:
\[ 70,150 = CP \times 0.7667 \]

### Step 6: Solve for Cost Price (CP)
To find the Cost Price (CP), rearrange the equation:
\[ CP = \frac{70,150}{0.7667} \]
Calculating this gives:
\[ CP \approx 91,500 \]

### Conclusion
The cost price of the article is approximately Rs. 91,500.

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