# PROFIT AND LOSS PROBLEMS

Problem 1 :

John bought a car for \$18000 and sold it to his friend for \$18900. Find the profit percentage.

Solution :

Profit = Selling price - Cost price

Profit = 18900 - 18000

Profit = 900

Profit % = (Profit/Cost price) ⋅ 100%

Profit % = (900/18000) ⋅ 100%

Profit % = 5%

Problem 2 :

Peter bought an item at \$300 and sold it for \$240. Find the loss percentage.

Solution :

Loss = Cost price - Selling price

Loss = 300 - 240

Loss = 60

Loss % = (Loss/Cost price) ⋅ 100%

Loss % = (60/300) ⋅ 100%

Loss % = 20 %

Problem 3 :

A sold a laptop to B at 15% profit. B sold the same laptop to C at 20% profit. If C had paid \$1656 for it, find the price at which A bought the laptop.

Solution :

Let x be the price at which A bought the laptop.

Cost price of B = 115% of x = 1.15x

Cost price of C = 120% of 1.15x = 1.38x

It is given that C paid \$1656.

Then, we have

1.38x = 1656

Divide both sides by 1.38

x = 1656/1.38

x = 1200

So, the price at which A bought the laptop is \$1200.

Problem 4 :

Michael sold an item at a loss of 5%. If he had sold at a profit of 20%, he would have got \$100 more. Find the cost is the cost price of the item.

Solution :

Let x be the cost price of the chair

S.P (-5%) = 95% of x

S.P (-5%) = 0.95x -----(1)

S.P (+10%) = 120% of x

S.P (+10%) = 1.2x -----(2)

In (2), he got \$100 more than (1).

Then, we have

(2) - (1) = 100

1.2x - 0.95x = 100

0.25x = 100

Divide both sides by 0.25

x = 100/0.25

x = 10000/25

x = 400

So, the cost price of the item is \$400.

Problem 5 :

A man bought 20 units of a product at the cost of \$400 and sold 5 units at the cost of \$125. Find the profit or loss percentage.

Solution :

Cost price for 20 units = \$400

Cost price for one unit = 400/20 = \$20

Selling price for 5 units = \$125

Selling price for one unit = 125/5 = \$25

Because selling price is more than cost price, there is profit.

Profit = Selling price - Cost price

Profit = 25 - 20

Profit = 5

Profit % = (Profit/Cost price) ⋅ 100%

Profit % = (5/20) ⋅ 100%

Profit % = 25%

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