Arithmetic

Profit & Loss

Easy

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

Entered answer:

✅ Correct Answer: 20000

Let us walk you through this step-by-step, making sure every part is crystal clear.

Given Information:

Total spent: Rs 50000

Desktop sold at 20% profit

Laptop sold at 10% loss

Overall profit: 2%

What we need to find: Purchase price of the desktop

When we sell something at a profit or loss, the selling price becomes a multiple of the purchase price:

20% profit means selling price = 1.2 × purchase price

10% loss means selling price = 0.9 × purchase price

2% overall profit means total selling price = 1.02 × total purchase price

Let's say the desktop costs x rupees.

Since total purchase = Rs 50000:

Desktop purchase price = x

Laptop purchase price = (50000 - x)

The crucial equation:

Total Selling Price = Desktop Selling Price + Laptop Selling Price

$1.02 \times 50000 = 1.2x + 0.9(50000 - x)$

The left side is our target (total selling price for 2% profit), and the right side adds up what we actually get from selling both items.

$1.2x + 0.9(50000 - x) = 1.02 \times 50000$

Calculate the right side:

$1.02 \times 50000 = 51000$

Expand the left side:

$1.2x + 0.9 \times 50000 - 0.9x = 51000$

$1.2x + 45000 - 0.9x = 51000$

Combine like terms:

$1.2x - 0.9x + 45000 = 51000$

$0.3x + 45000 = 51000$

Isolate x:

$0.3x = 51000 - 45000$

$0.3x = 6000$

$x = \dfrac{6000}{0.3} = \dfrac{6000}{\frac{3}{10}} = \dfrac{6000 \times 10}{3} = \dfrac{60000}{3} = 20000$

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

In profit-loss problems involving multiple items, set up an equation where the total selling price (calculated using overall profit) equals the sum of individual selling prices. This approach works for any number of items.

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A person spent Rs 500005000050000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20%20\%20% profit and the laptop at 10%10\%10% loss. If overall he made a 2%2\%2% profit then the purchase price, in rupees, of the desktop is

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CAT Past Year Questions (Topic-Wise)

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