If 20% more would be gained by selling an article for ₹ 93 than selling it for ₹ 85, then the cost price of the article is:

Options

A. ₹64
B. ₹40
C. ₹56
D. ₹60

Answer

To find the cost price (CP) of the article based on the given information, we can follow these steps:

### Step 1: Understand the problem
We know that selling the article for ₹93 yields a profit that is 20% more than the profit obtained by selling it for ₹85. We need to find the cost price of the article.

### Step 2: Define the profit from selling at two different prices
Let the cost price of the article be CP.

- Profit when sold for ₹85:
\[ \text{Profit}_1 = 85 - CP \]

- Profit when sold for ₹93:
\[ \text{Profit}_2 = 93 - CP \]

### Step 3: Set up the equation based on the given information
According to the problem, the profit from selling at ₹93 is 20% more than the profit from selling at ₹85. This can be expressed as:
\[ \text{Profit}_2 = \text{Profit}_1 + 0.2 \times \text{Profit}_1 \]
This simplifies to:
\[ \text{Profit}_2 = 1.2 \times \text{Profit}_1 \]

### Step 4: Substitute the profit expressions into the equation
Substituting the expressions for profit:
\[ 93 - CP = 1.2 \times (85 - CP) \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ 93 - CP = 1.2 \times 85 - 1.2 \times CP \]
Calculating \(1.2 \times 85\):
\[ 1.2 \times 85 = 102 \]
So the equation becomes:
\[ 93 - CP = 102 - 1.2 \times CP \]

### Step 6: Rearrange the equation to isolate CP
Rearranging gives:
\[ 93 - 102 = -1.2 \times CP + CP \]
\[ -9 = -0.2 \times CP \]
Dividing both sides by -0.2:
\[ CP = \frac{-9}{-0.2} = 45 \]

### Step 7: Conclusion
The cost price of the article is ₹45.