# 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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