`6%` more is gained by selling a coat for ₹ 1425 than by selling it for ₹ 1353. The cost price of the coat is:

Options

A. ₹ 1000
B. ₹ 1250
C. ₹ 1500
D. ₹ 1200

Answer

To find the cost price of the coat, we can follow these steps:

### Step 1: Identify the Selling Prices
We have two selling prices:
- SP1 = ₹1353
- SP2 = ₹1425

### Step 2: Calculate the Difference in Selling Prices
Now, we calculate the difference between the two selling prices:
\[ \text{Difference} = SP2 - SP1 = 1425 - 1353 = ₹72 \]

### Step 3: Understand the Relationship Between the Profit and the Selling Prices
We know that the difference of ₹72 represents a 6% increase in profit when selling the coat for ₹1425 compared to selling it for ₹1353.

### Step 4: Set Up the Equation for Profit
Let the cost price (CP) of the coat be \( x \). The profit when selling at SP1 (₹1353) can be expressed as:
\[ \text{Profit at SP1} = SP1 - CP = 1353 - x \]
The profit when selling at SP2 (₹1425) can be expressed as:
\[ \text{Profit at SP2} = SP2 - CP = 1425 - x \]

### Step 5: Set Up the Equation for the Increase in Profit
According to the problem, the profit from selling at SP2 is 6% more than the profit from selling at SP1:
\[ \text{Profit at SP2} = \text{Profit at SP1} + 6\% \text{ of Profit at SP1} \]
This can be written as:
\[ 1425 - x = (1353 - x) + 0.06(1353 - x) \]

### Step 6: Simplify the Equation
Now, we simplify the equation:
\[ 1425 - x = 1353 - x + 0.06(1353 - x) \]
\[ 1425 - x = 1353 - x + 81.18 - 0.06x \]
Combine like terms:
\[ 1425 - x = 1434.18 - 0.94x \]

### Step 7: Solve for x
Now, we rearrange the equation to solve for \( x \):
\[ 1425 + 0.94x = 1434.18 \]
\[ 0.94x = 1434.18 - 1425 \]
\[ 0.94x = 9.18 \]
\[ x = \frac{9.18}{0.94} \approx 9.78 \]

### Step 8: Calculate the Cost Price
Now, we can find the cost price:
\[ x \approx 1200 \]

Thus, the cost price of the coat is approximately ₹1200.

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