Aakash sells an article at a profit of 10%.Had he bought it for 5% less and sold it for 120 rs more then he would have gained 20% profit. What is the cost price of the article?

Options

A. A)Rs 2500
B. B)Rs 4000
C. C)Rs 3000
D. D)Rs 3500

Answer

To find the cost price of the article sold by Aakash, we can follow these steps:

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

### Step 2: Calculate the selling price (SP) with a 10% profit
If Aakash sells the article at a profit of 10%, the selling price will be:
\[ SP = CP + 10\% \text{ of } CP = x + 0.1x = 1.1x \]

### Step 3: Calculate the new cost price if bought for 5% less
If Aakash had bought the article for 5% less, the new cost price would be:
\[ New \, CP = CP - 5\% \text{ of } CP = x - 0.05x = 0.95x \]

### Step 4: Calculate the new selling price with a 20% profit
If he sells this article for Rs. 120 more than the original selling price, the new selling price would be:
\[ New \, SP = 1.1x + 120 \]
With a 20% profit on the new cost price, the new selling price can also be expressed as:
\[ New \, SP = New \, CP + 20\% \text{ of } New \, CP = 0.95x + 0.2(0.95x) = 0.95x + 0.19x = 1.14x \]

### Step 5: Set up the equation
Now, we can set the two expressions for the new selling price equal to each other:
\[ 1.1x + 120 = 1.14x \]

### Step 6: Solve for \( x \)
Rearranging the equation gives:
\[ 120 = 1.14x - 1.1x \]
\[ 120 = 0.04x \]
\[ x = \frac{120}{0.04} = 3000 \]

### Step 7: Conclusion
The cost price of the article is:
\[ \text{Cost Price} = Rs. 3000 \]