The cost price of two beds are equal. One bed is sold at a profit of `30%` and the other one ₹5504 less then the first one. If the overall profit earned after selling both the beds is `14%`, what is the cost price of each bed?

Options

A. ₹17000
B. ₹16800
C. ₹17600
D. ₹17200

Answer

To solve the problem step by step, we will denote the cost price of each bed as \( x \).

### Step 1: Define the Cost Price
Let the cost price of each bed be \( x \).

### Step 2: Calculate Selling Price of the First Bed
The first bed is sold at a profit of 30%. Therefore, the selling price (SP) of the first bed can be calculated as:
\[ SP_1 = x + 0.30x = 1.30x \]

### Step 3: Calculate Selling Price of the Second Bed
The second bed is sold for ₹5504 less than the first bed. Thus, the selling price of the second bed is:
\[ SP_2 = SP_1 - 5504 = 1.30x - 5504 \]

### Step 4: Calculate Total Selling Price
The total selling price of both beds is:
\[ SP_{total} = SP_1 + SP_2 = 1.30x + (1.30x - 5504) = 2.60x - 5504 \]

### Step 5: Calculate Overall Profit
The overall profit earned after selling both beds is 14%. Therefore, the total selling price can also be expressed in terms of the total cost price:
\[ SP_{total} = (Cost Price of both beds) + (14\% \text{ of Cost Price of both beds}) \]
Since the cost price of both beds is \( 2x \), we have:
\[ SP_{total} = 2x + 0.14 \times 2x = 2x(1 + 0.14) = 2.28x \]

### Step 6: Set Up the Equation
Now, we can set the two expressions for total selling price equal to each other:
\[ 2.60x - 5504 = 2.28x \]

### Step 7: Solve for \( x \)
Rearranging the equation gives:
\[ 2.60x - 2.28x = 5504 \]
\[ 0.32x = 5504 \]
Now, divide both sides by 0.32:
\[ x = \frac{5504}{0.32} = 17200 \]

### Conclusion
The cost price of each bed is ₹17,200.

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