A person purchased a cupboard and a cot for Rs. 18,000. He sold the cupboard at a profit of 20% and the cot at a profit of 30%. If his total profit was 25.833%, find the cost price of the cupboard.

Options

A. Rs. 10,500
B. Rs. 12,000
C. Rs. 7500
D. Rs. 10,000

Answer

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

### Step 1: Define Variables
Let the cost price of the cupboard be \( X \) and the cost price of the cot be \( Y \).

### Step 2: Set Up the Equation for Total Cost
According to the problem, the total cost of the cupboard and cot is:
\[ X + Y = 18000 \quad \text{(1)} \]

### Step 3: Calculate Selling Prices
The cupboard is sold at a profit of 20%, so the selling price (SP) of the cupboard is:
\[ SP_{cupboard} = X + 0.20X = 1.20X \]
The cot is sold at a profit of 30%, so the selling price of the cot is:
\[ SP_{cot} = Y + 0.30Y = 1.30Y \]

### Step 4: Calculate Total Selling Price
The total selling price of both items is:
\[ SP_{total} = SP_{cupboard} + SP_{cot} = 1.20X + 1.30Y \]

### Step 5: Calculate Total Profit
The total profit is given as 25.833% of the total cost:
\[ Total\ Profit = 0.25833 \times 18000 = 4669.94 \]
Thus, the total selling price can also be expressed as:
\[ SP_{total} = Total\ Cost + Total\ Profit = 18000 + 4669.94 = 22669.94 \]

### Step 6: Set Up the Equation for Total Selling Price
Now we can set up the equation:
\[ 1.20X + 1.30Y = 22669.94 \quad \text{(2)} \]

### Step 7: Solve the System of Equations
Now we have two equations:
1. \( X + Y = 18000 \) (1)
2. \( 1.20X + 1.30Y = 22669.94 \) (2)

From equation (1), we can express \( Y \) in terms of \( X \):
\[ Y = 18000 - X \quad \text{(3)} \]

### Step 8: Substitute Equation (3) into Equation (2)
Substituting equation (3) into equation (2):
\[ 1.20X + 1.30(18000 - X) = 22669.94 \]
Expanding this gives:
\[ 1.20X + 23400 - 1.30X = 22669.94 \]
Combining like terms:
\[ -0.10X + 23400 = 22669.94 \]
Subtracting 23400 from both sides:
\[ -0.10X = 22669.94 - 23400 \]
\[ -0.10X = -730.06 \]
Dividing both sides by -0.10:
\[ X = 7300.6 \]

### Step 9: Find the Cost Price of the Cot
Now substituting \( X \) back into equation (3) to find \( Y \):
\[ Y = 18000 - 7300.6 = 10699.4 \]

### Step 10: Final Answer
The cost price of the cupboard is approximately:
\[ \text{Cost Price of Cupboard} = Rs. 7300.60 \]