a computer company gives a discount of 10% on a new piece of software.If it makes a 40% profit what percentage does the marked price exceed the cost price
To find the percentage that the marked price exceeds the cost price, we need to first calculate the cost price of the software after the 10% discount is applied.
Let's say the marked price of the software is X. After a 10% discount, the selling price (cost price) of the software will be 90% of X, which can be calculated as:
Cost price = X - (10/100) * X
= X - (0.1) * X
= X(1 - 0.1)
= 0.9X
Now, we are given that the company makes a 40% profit on the cost price. So, the selling price will be 40% greater than the cost price.
Selling price = Cost price + Profit
= 0.9X + (40/100) * 0.9X
= 0.9X + (0.4) * 0.9X
= 0.9X + 0.36X
= 1.26X
Now, to find the percentage that the marked price exceeds the cost price, we need to calculate the percentage increase from the cost price to the selling price:
Percentage increase = (Selling price - Cost price) / Cost price * 100
= (1.26X - 0.9X) / 0.9X * 100
= 0.36X / 0.9X * 100
= 0.4 * 100
= 40%
Therefore, the marked price exceeds the cost price by 40%.