A man sells an article at a gain of 25%. If he had bought it at 20% less and sold it for 5 less, he would have gained 45%. The cost price of the article is

Options

A. 81
B. 500/9
C. 80
D. 78

Answer

To find the cost price (CP) of the article, we can break down the problem step by step.

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

### Step 2: Selling Price with 25% Gain
If the man sells the article at a gain of 25%, the selling price (SP) can be calculated as:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 3: Adjusted Cost Price
If he had bought it at 20% less, the new cost price would be:
\[ New \, CP = CP - 0.20 \times CP = 0.80 \times CP \]

### Step 4: Selling Price with 45% Gain
If he sold it for Rs. 5 less than the original selling price, the new selling price would be:
\[ New \, SP = SP - 5 = 1.25 \times CP - 5 \]
According to the problem, this new selling price gives him a gain of 45% on the new cost price:
\[ New \, SP = New \, CP + 0.45 \times New \, CP = 1.45 \times New \, CP \]
Substituting the new cost price:
\[ New \, SP = 1.45 \times (0.80 \times CP) = 1.16 \times CP \]

### Step 5: Set Up the Equation
Now, we can set the two expressions for the new selling price equal to each other:
\[ 1.25 \times CP - 5 = 1.16 \times CP \]

### Step 6: Solve for CP
Rearranging the equation:
\[ 1.25 \times CP - 1.16 \times CP = 5 \]
\[ 0.09 \times CP = 5 \]
\[ CP = \frac{5}{0.09} = \frac{500}{9} \]

### Step 7: Final Answer
Thus, the cost price of the article is:
\[ CP = \frac{500}{9} \approx 55.56 \]