## PROFIT AND LOSS PRACTICE PROBLEMS

Profit and Loss Practice Problems :

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 :

A man buys a cycle for \$1400 and sells it at a loss of 15%. What is the price of the cycle ?

Solution :

A man sells the cycle for 85% of cost price to make 15% loss.

=  85% of 1400

=  1190

Hence the cost of bicycle is 1190.

Example 2 :

Peter purchased a machine for \$80000 and spent \$5000 on repair and \$1000 on transport and sold it with 25% profit. At what price did he sell the machine ?

Solution :

The cost price of the machine  =  \$80000

Repairing charge  =  \$5000

Transport charge  =  \$1000

Total cost  =  80000 + 5000 + 1000

=  86000

Selling price of machine  =  125% of 86000

=  107500

Hence the cost of the machine is 107500.

Example 3 :

A shopkeeper expects a gain of 22  1/2% on his cost price. If in a week, his sale was \$392, what was the profit ?

Solution :

Let x be the cost price.

122.5% of x  =  392

1.225x  =  392

x  =  392/1.225

x  =  320

Profit  =  Selling price - Cost price

=  392 - 320

Profit  =  72

Hence the required profit is 72.

Example 4 :

A manufacturer undertakes to supply 2000 pieces of a particular component at \$25 per piece. According  to his estimates even if 5% fail to pass the quality tests, then he will make a profit of 25%. However as it turned out, 50% of the components were rejected. What is the loss of the manufacturer ?

Solution :

Let x be the the total cost of production.

Total cost of production  =  25x

Total number of components undertaken  =  2000

Cost of each component  =  \$25

5% of components fails in quality test

Number of components failed in the quality check

=  5% of 2000

=  100

Number of components passed in the quality check

=  2000 - 100

=  1900

Cost price of 1900 components  =  1900(25)

=  47500

Even if 5% fails in the quality test, then he will make a profit of 25%.

125% of x  =  47500

x  =  47500(100/125)

x  =  38000

50% of the components passed in the quality check.

50% of 2000  =  1000

Cost of 1000 products  =  25(1000)

=  25000

Difference between total cost production and cost of production of 50% of the components undertaken

=  38000 - 25000

=  13000

Hence the loss is 13000.

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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