## SOLVED PROBLEMS ON PROFIT AND LOSS

Solved Problems on Profit and Loss :

In this section, we will see how to solve problems with the concept of profit and loss.

## Formulas Used in Profit and Loss

Profit (or) gain  =  Selling price - Cost price

Loss  =  Cost price - Selling price

Profit %  =  (Profit / Cost price) ⋅ 100

Loss %  =  (Loss / Cost price) ⋅ 100

Cost price  =  [100 / (100 - loss%)] ⋅ Selling price

Cost price  =  [100 / (100 + profit%)] ⋅ Selling price

Selling price  =  [(100 + profit%)/100] ⋅ Cost price

Selling price  =  [(100 - loss%)/100] ⋅ Cost price

## Profit and Loss Practice Problems - Examples

Example 1 :

The product is marked at 20% above the cost price. It is then sold at 90% of the selling price. The profit is \$120. What is the cost price of this product.

Solution :

Let x be the the cost price.

120% of x  = Marked price

Selling price  =  90% of marked price

=  90% of (120% of x)

=  0.90(1.2x)

=  1.08x

Profit  =  \$120 ---(1)

Profit  =  Cost price - Selling price

=  x - 1.08x

=  x(1 - 1.08)

Profit  =  0.08x  ---(2)

(1)  =  (2)

0.08x  =  120

x  =  120/0.08

x  =  1500

Hence the cost price is 1500.

Example 2 :

A shop purchased some shoes at \$65 per pair. It then sold them at \$74 per pair. The shopkeeper calculated that the profit earned was \$440 when there were 5 pairs of shoes left. How many pairs of shoes did the shop purchase initially ?

Solution :

Let x be the number of pair of shoes in the shop.

Pair of shoes left  =  5

Cost price of pair of shoes going to be sold  =  65x

Selling price of pair of shoes has been sold  =  74(x - 5)

Profit  =  440

Profit  =  Selling price - Cost price

74(x - 5) - 65x  =  440

74x - 370 - 65x  =  440

9x  =  440 + 370

9x  =  810

x  =  810/9

x  =  90

So, the shop purchased 90 pairs of shoes initially.

Example 3 :

The selling price of a sofa set is \$12000. It is later sold at \$6500 at an exhibition. The profit made is 30%. What is the percentage of profit if the profit is \$5000 ?

Solution :

Selling price of a sofa  =  12000

By selling the sofa at the cost of \$6500, it made a profit 30%.

Let x be the cost price of sofa.

130% of x  =  6500

1.30x  =  6500

x  =  6500/1.30

x  =  5000

Cost price of sofa is 5000.

Profit %  =  (Profit / cost price)  ⋅ 100

=  (5000/5000) ⋅ 100

=  100%

After having gone through the stuff given above, we hope that the students would have practiced problems in profit and loss.

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