PROFIT AND LOSS PRACTICE PROBLEMS

Problem 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

So, the cost of bicycle is 1190.

Problem 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

So, the cost of the machine is 107500.

Problem 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

So, the required profit is 72.

Problem 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

So, the loss is 13000.

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