CAT 2020 Slot 1 QA Question & Solution
ArithmeticEasy
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
Solution
Let the price of the desktop and laptop be $x$ and $y$, respectively.
It is given that:
$$
x + y = 50000 \quad \text{...(i)}
$$
$$
1.2x + 0.9y = 50000 \times 1.02 = 51000 \quad \text{...(ii)}
$$
Subtracting $0.9 \times (i)$ from (ii):
$$
1.2x + 0.9y - 0.9(x + y) = 51000 - 0.9 \times 50000
$$
$$
1.2x + 0.9y - 0.9x - 0.9y = 51000 - 45000
$$
$$
0.3x = 6000 \implies x = 20000
$$
Therefore, the price of the desktop is ₹20,000.