WORD PROBLEMS ON PROFIT AND LOSS
In this section, you will learn how to solve profit and loss word problems.
Before look at the word problems profit and loss, if you would like to learn the shortcuts on profit and loss,
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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