A computer company gives a discount of 10% off of the marked price on a new
piece of software. If it makes a profit of 11% on this sale, what percent does the
marked price exceed the cost price?
sale price = 1.11 cost
sale price = 0.90 marked price
so
0.90 marked price = 1.11 cost
or
marked price = 1.23 cost
so 23 %
To find the answer to this question, we need to break it down into steps:
Step 1: Find the selling price after the 10% discount.
Step 2: Calculate the profit made on this sale.
Step 3: Find the percentage by which the marked price exceeds the cost price.
Let's dive into each step:
Step 1: Find the selling price after the 10% discount.
To calculate the selling price after the 10% discount, we need to subtract 10% of the marked price from the marked price:
Selling price = Marked price - 10% of Marked price
= Marked price - (10/100) * Marked price
= Marked price * (1 - 10/100)
= Marked price * 0.9
Step 2: Calculate the profit made on this sale.
The profit made on the sale can be calculated by subtracting the cost price from the selling price:
Profit = Selling price - Cost price
Step 3: Find the percentage by which the marked price exceeds the cost price.
To find the percentage by which the marked price exceeds the cost price, we can use the following formula:
Percentage increase = (Gain or Profit / Cost price) * 100
For this particular scenario, we know the profit percentage is 11%. So, we can replace the profit with 11% of the cost price in the formula above.
Now, let's put it all together and solve the problem.
Given that the profit is 11%, we can equate the profit to 11% of the cost price:
Profit = 11% of Cost price
Now, using step 2, we know that Profit = Selling price - Cost price. Therefore,
11% of Cost price = Selling price - Cost price
Now, let's substitute the value of Selling price from step 1:
11% of Cost price = (Marked price * 0.9) - Cost price
Now, let's solve the equation for the marked price exceeding the cost price:
(11/100) * Cost price = (Marked price * 0.9) - Cost price
(11/100) * Cost price + Cost price = Marked price * 0.9
((11/100) + 1) * Cost price = Marked price * 0.9
((11 + 100) / 100) * Cost price = Marked price * 0.9
(111/100) * Cost price = Marked price * 0.9
Marked price = ((111/100) * Cost price) / 0.9
Finally, to find the percentage by which the marked price exceeds the cost price, we can divide the difference (Marked price - Cost price) by the cost price, and then multiply by 100:
Percentage increase = ((Marked price - Cost price) / Cost price) * 100
By substituting the values in the above formula, we can find the desired percentage.