Question

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is [This Question was asked as TITA]

• A. 10000
• B. 40000
• C. 20000
• D. 30000

Answer 1

The Correct Option is C

Let the purchase price of the desktop be Rs \( x \).
Then, the purchase price of the laptop is Rs \( 50000 - x \).

The desktop is sold at a profit of 20%, so the selling price of the desktop is:
\( \text{Selling Price of Desktop} = x + 0.2x = 1.2x \).

The laptop is sold at a loss of 10%, so the selling price of the laptop is:
\( \text{Selling Price of Laptop} = (50000-x) - 0.1(50000-x) = 0.9(50000-x) \).

He made an overall profit of 2%, so the total selling price is:
\( \text{Total Selling Price} = 50000 + 0.02 \times 50000 = 51000 \).

Thus, the equation becomes:
\( 1.2x + 0.9(50000-x) = 51000 \).

Simplifying:
\( 1.2x + 45000 - 0.9x = 51000 \)
\( 0.3x = 6000 \)
\( x = \frac{6000}{0.3} = 20000 \).

Therefore, the purchase price of the desktop is Rs 20000.

Answer 2

Let the price of the desktop be \( x \) and the price of the laptop be \( y \). 

The total cost of one desktop and one laptop is:
\( x + y = 50,000 \)     \( \cdots \text{(1)} \)

According to the given condition, the cost of 12 desktops and one laptop after a 10% discount is equal to 2% more than the original total:
\( 12x + 0.9y = 50,000 \times 1.02 \)
\( 12x + 0.9y = 51,000 \)     \( \cdots \text{(2)} \)

Solving equations (1) and (2):

From equation (1), we get:
\( y = 50,000 - x \)

Substituting into equation (2):
\( 12x + 0.9(50,000 - x) = 51,000 \)
\( 12x + 45,000 - 0.9x = 51,000 \)
\( 11.1x = 6,000 \)
\( x = \frac{6,000}{11.1} = 20,000 \)

Therefore, the price of the desktop is \( \boxed{20,000} \).

Correct Option: (C) 20,000