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

Answer 1

Using Alligation Rule, the ratio of cost prices of desktop and laptop will be

Let the total cost be ₹50,000. 

We are told that the cost of the desktop is \(\frac{2}{5}\) of the total cost.

So, the cost of the desktop is: \[ \text{Cost of desktop} = \frac{2}{5} \times 50000 \] Now calculate the product: \[ = \frac{2 \times 50000}{5} = \frac{100000}{5} = 20000 \] ∴ The cost of the desktop is ₹20,000.

Answer 2

Let D be the cost of the desktop and L be the cost of the laptop.

Step 1: Given equations

• From the statement: "0.2 times D minus 0.1 times L is equal to 2% of ₹50,000": \[ 0.2D - 0.1L = 0.02 \times 50000 = 1000 \tag{1} \]
• Multiplying equation (1) by 10 to eliminate decimals: \[ 2D - L = 10000 \tag{2} \]
• We are also given that the total cost of the desktop and laptop is ₹50,000: \[ D + L = 50000 \tag{3} \]

Step 2: Solving the system

Add equations (2) and (3):

\[ 2D - L + D + L = 10000 + 50000 \] \[ 3D = 60000 \] \[ D = \frac{60000}{3} = \boxed{20000} \]

 Final Answer: \( \boxed{D = 20000} \)