Problem 1 :
Cindy bought 50 pens for $100. She then sold each pen for $2.50. Find the profit or loss percentage.
Solution :
Cost price of 50 pens = $100
Cost price of 1 pen = 100/50 = $2
Selling price of 1 pen = $2.50
Because the selling price of 1 pen is more than cost price of 1 pen, there is profit.
Finding Profit :
Profit = Selling price - Cost price
Profit = 2.50 - 2
Profit = 0.50
Finding Profit Percentage :
Profit % = (Profit/Cost price) ⋅ 100 %
Profit % = (0.50/2) ⋅ 100 %
Profit % = 25 %
Problem 2 :
Jacob purchased a house for $49,000. He spent $6000 for repair and $5,000 for air-conditioning. If he had sold the house $58,000, find the gain or loss percentage in this transaction. (If it is needed, round your answer to the nearest hundredths)
Solution :
Total amount spent on the house is
= 49,000 + 6,000 + 5,000
= 60,000
This is the cost price of the house ($60,000).
Selling price of the house = $58,000
Because the selling price of the house is less than the cost price, there is loss.
Finding Loss :
Loss = Cost price - Selling price
Loss = 60,000 - 58,000
Loss = 2,000
Finding Loss Percentage :
Loss % = (Loss/Cost price) ⋅ 100 %
Loss % = (2000/60000) ⋅ 100 %
Loss % = 3.33 %
Problem 3 :
Goods are purchased for $1500. If one fifth of the goods sold at a profit of 5% and the remaining four-fifth of the goods at a profit of 10%, find the net profit percentage.
Solution :
Cost price of one-fifth of the goods is
= 1/5 ⋅ 1500
= 300
Selling price of one-fifth of the goods (at 5% profit) is
= (100 + 5)% of 300
= 105% of 300
= 1.05 ⋅ 300
= 315
Cost price of remaining four-fifth of the goods is
= 4/5 ⋅ 1500
= 1,200
Selling price of the remaining four-fifth of the goods (at 10% profit) is
= (100 + 10)% of 1200
= 110% of 1200
= 1.10 ⋅ 1200
= 1,320
Selling price of the total goods
= 315 + 1,320
= 1,635
Finding Net Profit :
Net profit = S.P of total goods - C.P of total goods
Net Profit = 1635 - 1500
Net Profit = 135
Finding Net Profit Percentage :
Net profit % = (Net profit/Cost price) ⋅ 100 %
Net profit % = (135/1500) ⋅ 100 %
Net profit % = 9 %
Problem 4 :
A trader bought a product for $200. If marks his goods 20% above the cost price and gives a discount of 10% for cash, find his profit percentage
Solution :
Cost price of the product = $100
Marked price (20% above the cost price) is
= (100 + 20) % of 200
= 120% of 200
= 1.2 ⋅ 200
= 240
Selling price price is the price which is after 20% discount from the marked price.
So, the selling price is
= (100 - 10) % of Marked price
= 90% of 240
= 0.9 ⋅ 240
= 216
Finding Profit :
Profit = Selling price - Cost price
Profit = 216 - 200
Profit = 16
Finding Profit Percentage :
Profit % = (Profit/Cost price) ⋅ 100 %
Profit % = (16/200) ⋅ 100 %
Profit % = 8 %
Problem 5 :
A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.
Solution :
Let the cost price be $100.
Then, the selling price (at 20% profit) is
= (100 + 20)% of 100
= 120% of 100
= 1.2 ⋅ 100
= 120
Selling price is the price which is after 20% discount from the marked price.
It has been illustrated in the picture given below.
From the above picture, we get
Selling price = (100 - 20)% of Mmarked price
120 = 80% of x
120 = 0.8 ⋅ x
Divide both sides by 0.8
120/0.8 = x
1200/8 = x
150 = x
So, the marked price is $150.
Here,
Cost price = $100
Marked Price = $150
Hence, the required percentage increase is 50%
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