moses paid sh 150 for a shirt after getting a discount of 10 percent. the shopkeeper made a profit of 20 percent on the sale of the shirt. what percentage would the shopkeeper have made if no discount was allowed?
Moses paid sh 150 for a shirt after getting a discount of 10 percent mean:
sh 150 = 100% - 10% = 90% = 90 /100 = 0.9 of original price
sh150 = 0.9 of original price
Divide both sides by 0.9
sh150 / 0. 9 = 0.9 of original price / 0.9
sh 166.666 = original price
The shopkeeper made a profit of 20 percent on the sale of the shirt.
20 percent = 20% = 20 / 100 = 0.2
The shopkeeper made a profit of 0.2 ∙ 166.666 = sh 33.333 if no discount was allowed.
To find the percentage profit the shopkeeper would have made if no discount was allowed, we first need to calculate the original selling price of the shirt before the discount.
Let's assume the original selling price of the shirt is "x" shillings.
Since Moses paid 150 shillings after a 10% discount, it means that the selling price after the discount is 90% of the original price:
90% of x = 150 shillings
To find x, we need to divide 150 shillings by 90% expressed as a decimal (0.90):
x = 150 shillings / 0.90
x ≈ 166.67 shillings (rounded to two decimal places)
So, the original selling price of the shirt before the discount was approximately 166.67 shillings.
Now, we can calculate the profit percentage the shopkeeper made. We know that the shopkeeper made a 20% profit on the sale of the shirt.
Profit percentage = (Profit / Cost Price) * 100
The profit is calculated as the selling price minus the cost price.
Cost price = original selling price = 166.67 shillings
Selling price = 150 shillings (after the discount)
Profit = Selling price - Cost price = 150 shillings - 166.67 shillings
Profit percentage = (Profit / Cost price) * 100 = ((150 - 166.67) / 166.67) * 100
Calculating this:
Profit percentage ≈ (-16.67 / 166.67) * 100 ≈ -10%
The negative sign indicates that the shopkeeper would have made a loss of approximately 10% if no discount was allowed.