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

Calculation:

Let the CP (Purchase Price) of the desktop be Rs.x

So, the CP of the laptop = Rs.(50000 – x)

Hence, the SP of the desktop is calculated as:

SP_desktop = [(100 + 20)/100] × x = 1.2x

Similarly, for the laptop,

SP_laptop = [(100 – 10)/100] × x = 0.9 × (50000 – x)

⇒ SPlaptop = 45000 – 0.9x

Hence, the total SP = (45000 – 0.9x) + 1.2x = 0.3x + 45000      ----(iv)

Also, the total CP = Rs.50000      ----(v)

So, from the relation for Profit%, we get:

⇒ 2 = [(0.3x + 45000 – 50000)/50000] × 100 

⇒ 2 = [(0.3x – 5000)/500]

⇒ 0.3x = 6000

⇒ x = 20000

∴ The Purchase Price of the desktop is Rs. 20000

 

If SP = Selling Price, and CP = Cost Price. Then:

%Profit = [(SP – CP)/CP] × 100      ----(i)

If an article is sold at a Loss of a%:

SP = [(100 – a)/100] × CP      ----(ii)

Similarly, if the article is sold at a Profit of a%:

SP = [(100 + a)/100] × CP      ----(iii)