Profit and loss formulas with exmaples for SSC and bank exams

Students who are recently passed senior secondary memorize the profit and loss formulas with examples for SSC and Bank exams. Often students make mistake to use profit and loss formulas. If you preparing for competitive exams, you should understand properly how to use profit and loss formulas.

Here in this blog, you can learn easily how to use profit and loss formulas correctly with examples in your competitive exams. You can learn solutions of profit and loss problems also.

Profit and Loss Formulas for Competitive exams with Examples:

Cost Price (CP) 

The money paid by the shopkeeper to the manufacture or money paid by the customer to the shopkeeper is called the cost price (CP) of the goods

$$ CP \  =  \left( {100\over100+Gain \ percent}\right)×SP,CP = \left( {100\over100-Loss \ percent}\right)×SP $$

* If an article is purchased for some amount and there are some additional expenses on transportation, labor, commission etc. these are to be added in the cost price. Such expenses are called overhead expenses.

Selling Price (SP)

The price at which the shopkeeper sells the goods is called the selling price (SP).

 $$ SP \  =  \left( {100+Gain \ percent\over100}\right)×CP,SP = \left( {100-Loss \ percent\over100}\right)×CP $$

Profit or Gain 

Whenever a person sells an article at price greater than the cost price, he is said to have made a profit or gain.

Profit or Gain = SP – CP [SP > CP]

 $$ Profit \ percent \ =   {Profit\over Cost\ price}× 100\% = {P\over CP}× 100\% $$

Loss

If the selling price of an article is less than its cost price, then the shopkeeper suffers a loss.

Loss =CP – SP [CP>SP]

 $$ Loss \ percent \ =   {Loss\over Cost\ price}× 100\% = {L\over CP}× 100\% $$

1. If a person sells two similar articles, one at a gain of a% and another at a loss of a%, then the seller always incurs a loss which is given by $$ Loss \ percent = \left({a\over10}\right)^2 \%   $$

Example.1. A man sold two radios for Rs. 2000 each. On one he gains 16% and on the other, he loses 16%. Find his gain or loss percent in the whole transaction.

Solution:

According to the formula $$ Loss \ percent =     \left({a\over10}\right)^2  =\left({16\over10}\right)^2  = {256\over100} = 2.56 \% $$

2. If a dishonest trader professes to sell his item at CP but uses false weight, then

$$ Gain \ Percent = {Error\over True Value - Error}× 100 \%   $$

  $$ or\  Gain \ Percent = {True\ weight - False\ weight\over False \ Weight}× 100 \%  $$

 Example.2.A dishonest dealer professes to sell his good at cost price but he uses a weight of 930 g for a kg weight. Find his gain percent.

Solution:

According to the formula

$$ Gain \ Percent = {Error\over True Value - Error}× 100   $$

  $$  = {70\over 1000 - 70}× 100    $$

   $$  = {70\over 930 }× 100    $$

  $$  = {700\over 93 }  =7{49\over 93 }\%   $$

3. If cost price of a articles is equal to the selling price of b articles, then $$ Profit\ percent =      {a -b\over b}×100 \%  $$

 Example.3. If the cost price of 20 articles is equal to the selling price of 18 articles, find the profit per cent.

Solution: 

Given that , a = 20, b = 18

According to the formula

  $$ Profit\ percent =     \left({a -b\over b}×100\right)\%  $$

   $$  =     \left({20 -18\over 18}×100\right)\%  $$

  $$  =     {100 \over 9}=11{1 \over 9} \% $$

4. A tradesman mark his good at a% above the cost price and give purchases at discount of b% for cash then there is % profit or loss according to (+) ve or (-) ve sign.

 Example.4. A tradesman marks his good at 20% above the cost price and allows purchases a discount of 10% for cash. What profit percent does he make?

Solution: 

Given that, a= 20% b=10%

According to the formula,

Required answer =  $$ Required \ answer =    \left(a-b-{ab\over100}\right)= \left(20-10-{20×10\over100}  \right)$$ $$ =(20-18)=8 \% Profit$$

Here, (+)ve sign shows that there is a profit.

5. A business sells his items at a profit of a%. If he had sold it for R more, he would have gained b%. Then,

$$ CP \ Of \ Items = {R\over b - a}× 100   $$

Example.5.A person sold a table at a profit of %. If he had sold it for Rs 1250 more, he would have gained 19%. Find the CP of the table.

Solution

Here, a = %.   = %, b = 19%, R= Rs.1250

According to the formula

$$ CP \ Of \ Table = {R\over b - a}× 100   $$

   $$  = {1250\over 19 - {13\over2}}× 100   $$

  $$  = {1250×2\over 25}× 100  = 10000 $$

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