An article was sold at 20% profit. Had it purchased at Rs 20 less and sold at Rs 20 less there would have been profit of 10% more. 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 20% Profit
If the article is sold at a profit of 20%, then the selling price (S.P.) can be calculated as:
\[ S.P. = C + 0.2C = 1.2C \]

### Step 3: Adjust the Cost Price and Selling Price
According to the problem, if the cost price was Rs. 20 less, the new cost price would be:
\[ C' = C - 20 \]
If the selling price was also Rs. 20 less, the new selling price would be:
\[ S.P.' = S.P. - 20 = 1.2C - 20 \]

### Step 4: Calculate New Profit Percentage
The problem states that with the new cost price and selling price, there would be a profit of 10% more than the original profit. The original profit was 20%, so the new profit percentage is:
\[ 20\% + 10\% = 30\% \]
Thus, the new selling price can also be expressed as:
\[ S.P.' = C' + 0.3C' = 1.3C' \]

### Step 5: Set Up the Equation
Now we can set the two expressions for the new selling price equal to each other:
\[ 1.2C - 20 = 1.3(C - 20) \]

### Step 6: Expand and Simplify
Expanding the right side gives:
\[ 1.2C - 20 = 1.3C - 26 \]
Now, rearranging the equation:
\[ 1.2C - 1.3C = -26 + 20 \]
\[ -0.1C = -6 \]

### Step 7: Solve for C
Dividing both sides by -0.1:
\[ C = \frac{-6}{-0.1} = 60 \]

### Conclusion
The cost price of the article is:
\[ \boxed{60} \]