An article was sold at 25% profit. Had it purchased at Rs 20 less and sold at Rs 10 less there would have been profit of 5% 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 the variables
Let the Cost Price (C.P.) of the article be \( x \).

### Step 2: Calculate the Selling Price (S.P.)
Since the article is sold at a profit of 25%, the Selling Price (S.P.) can be calculated as:
\[ S.P. = C.P. + 25\% \text{ of } C.P. = x + 0.25x = 1.25x \]

### Step 3: Set up the new cost price and selling price
If the article was purchased at Rs. 20 less, the new C.P. would be:
\[ \text{New C.P.} = x - 20 \]
If it was sold at Rs. 10 less, the new S.P. would be:
\[ \text{New S.P.} = 1.25x - 10 \]

### Step 4: Determine the new profit percentage
According to the problem, the new profit is 5% more than the original profit of 25%. Thus, the new profit percentage is:
\[ 25\% + 5\% = 30\% \]
This means:
\[ \text{New S.P.} = \text{New C.P.} + 30\% \text{ of New C.P.} \]
Substituting the values:
\[ 1.25x - 10 = (x - 20) + 0.30(x - 20) \]

### Step 5: Simplify the equation
Now, simplify the right-hand side:
\[ 1.25x - 10 = (x - 20) + 0.30x - 6 \]
\[ 1.25x - 10 = 1.30x - 26 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ 1.25x - 1.30x = -26 + 10 \]
\[ -0.05x = -16 \]

### Step 7: Solve for x
Dividing both sides by -0.05:
\[ x = \frac{-16}{-0.05} = 320 \]

### Step 8: Conclusion
Thus, the Cost Price (C.P.) of the article is:
\[ \text{C.P.} = Rs. 320 \]

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