Gyanendra sold article at 25% profit Ifhe buys it is Rs 600 less and sells it in Rs 600 less then earn 5% more profit. Find the original C.P.

Options

A. Rs 3600
B. Rs 4000
C. Rs 5000
D. Rs 5600

Answer

To solve the problem step-by-step, let's break it down:

### Step 1: Understand the given information
Gyanendra sold an article at a profit of 25%. If he buys it for Rs 600 less and sells it for Rs 600 less, he earns 5% more profit.

### Step 2: Define the variables
Let the original cost price (C.P.) be \( 4x \).
Then, the selling price (S.P.) at 25% profit can be calculated as:
\[ \text{S.P.} = \text{C.P.} + \text{Profit} = 4x + 0.25 \times 4x = 4x + x = 5x \]

### Step 3: Calculate the new cost price and selling price
If he buys the article for Rs 600 less, the new cost price becomes:
\[ \text{New C.P.} = 4x - 600 \]
If he sells it for Rs 600 less, the new selling price becomes:
\[ \text{New S.P.} = 5x - 600 \]

### Step 4: Calculate the new profit percentage
The new profit percentage is 5% more than the original 25%, which is:
\[ \text{New Profit %} = 25\% + 5\% = 30\% \]
This means:
\[ \text{New Profit} = 30\% \text{ of New C.P.} = 0.30 \times (4x - 600) \]

### Step 5: Set up the equation for new profit
The new selling price can also be expressed in terms of the new cost price and new profit:
\[ \text{New S.P.} = \text{New C.P.} + \text{New Profit} \]
Substituting the values:
\[ 5x - 600 = (4x - 600) + 0.30 \times (4x - 600) \]

### Step 6: Simplify the equation
Expanding the right side:
\[ 5x - 600 = (4x - 600) + (1.2x - 180) \]
Combining like terms:
\[ 5x - 600 = 4x + 1.2x - 600 - 180 \]
\[ 5x - 600 = 5.2x - 780 \]

### Step 7: Rearranging the equation
Rearranging gives:
\[ 5x - 5.2x = -780 + 600 \]
\[ -0.2x = -180 \]
\[ x = \frac{-180}{-0.2} = 900 \]

### Step 8: Calculate the original cost price
Now, substituting \( x \) back to find the original cost price:
\[ \text{Original C.P.} = 4x = 4 \times 900 = 3600 \]

### Final Answer
The original cost price is Rs 3600.

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