The cost price of item B is ₹180 more than cost price of item A. Item A was sold at a profit of `20%` and. item B was sold at a loss of `40%`. if the respective ratio of selling prices of items A and B is `5 :4`, what is the cost price of item A?

Options

A. ₹300
B. ₹360
C. ₹380
D. ₹320

Answer

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

### Step 1: Define the Variables
Let the cost price of item A be \( x \). Therefore, the cost price of item B will be \( x + 180 \).

### Step 2: Calculate Selling Prices
- Item A is sold at a profit of 20%. Therefore, the selling price (SP) of item A can be calculated as:
\[ SP_A = x + 0.2x = 1.2x \]

- Item B is sold at a loss of 40%. Therefore, the selling price of item B can be calculated as:
\[ SP_B = (x + 180) - 0.4(x + 180) = 0.6(x + 180) = 0.6x + 108 \]

### Step 3: Set Up the Ratio
We know that the ratio of the selling prices of items A and B is \( 5:4 \). Thus, we can write:
\[ \frac{SP_A}{SP_B} = \frac{5}{4} \]
Substituting the expressions for \( SP_A \) and \( SP_B \):
\[ \frac{1.2x}{0.6x + 108} = \frac{5}{4} \]

### Step 4: Cross Multiply
Cross multiplying gives us:
\[ 4 \cdot 1.2x = 5 \cdot (0.6x + 108) \]
This simplifies to:
\[ 4.8x = 3x + 540 \]

### Step 5: Solve for \( x \)
Rearranging the equation:
\[ 4.8x - 3x = 540 \]
\[ 1.8x = 540 \]
Dividing both sides by 1.8:
\[ x = \frac{540}{1.8} = 300 \]

### Step 6: Conclusion
The cost price of item A is \( \text{₹} 300 \).