An article was sold at 23% profit. Had it purchased at Rs 4 less and sold at Rs 20 less there would have been profit of 10% less. Find C.P. of article?

Answer

To find the cost price (C.P.) of the article, we can follow these steps:

### Step 1: Define Variables
Let the cost price of the article be \( C \).

### Step 2: Calculate Selling Price with 23% Profit
The selling price (S.P.) when sold at a 23% profit can be calculated as:
\[ S.P. = C + 0.23C = 1.23C \]

### Step 3: Calculate New Cost Price and Selling Price
If the article was purchased at Rs 4 less, the new cost price would be:
\[ C - 4 \]
If it was sold at Rs 20 less, the new selling price would be:
\[ 1.23C - 20 \]

### Step 4: Determine the New Profit Percentage
According to the problem, if the article was purchased at Rs 4 less and sold at Rs 20 less, the profit would be 10% less than the original profit of 23%. Therefore, the new profit percentage would be:
\[ 23\% - 10\% = 13\% \]

### Step 5: Write the Equation for New Profit
The profit when sold at the new selling price can be expressed as:
\[ \text{New Profit} = \text{New Selling Price} - \text{New Cost Price} \]
This gives us:
\[ (1.23C - 20) - (C - 4) = 0.13(C - 4) \]

### Step 6: Simplify the Equation
Expanding the left side:
\[ 1.23C - 20 - C + 4 = 0.13C - 0.52 \]
This simplifies to:
\[ 0.23C - 16 = 0.13C - 0.52 \]

### Step 7: Rearrange the Equation
Rearranging the equation gives:
\[ 0.23C - 0.13C = 16 - 0.52 \]
\[ 0.10C = 15.48 \]

### Step 8: Solve for C
Now, divide both sides by 0.10:
\[ C = \frac{15.48}{0.10} = 154.8 \]

### Conclusion
The cost price (C.P.) of the article is Rs 154.8.