PROFIT AND LOSS

IMPORTANT DEFINATIONS AND FORMULAE :-

1.   Cost Price :-  The price at which a product is bought is called its cost price. Cost price is written as CP.

2.   Selling Price :-  The amount got when an object is sold is called selling price. Selling price is written as SP.

3.   Profit or Gain :-  If  SP > CP,  then the difference between SP - CP is known as profit or gain.

4.   Loss :-  If  SP < CP,  then the difference between CP - SP is known as loss.

         Profit = SP - CP
         Loss = CP - SP
         SP = Profit + CP
         CP = SP - Profit

5.   Gain %  = $\frac{Gain}{CP}\times 100$

6.   Loss %  = $\frac{Loss}{CP}\times 100$

7.   SP = $\frac{\left ( 100\, +\, Gain \, \% \right )}{100}\times CP$

8.   SP = $\frac{\left ( 100\, -\, Loss \, \% \right )}{100}\times CP$

9.   CP = $\frac{100}{\left ( 100\, +\, Gain\, \% \right )}\times SP$

10. CP = $\frac{100}{\left ( 100\, -\, Loss\, \% \right )}\times SP$

11. If a dealer sells his goods at cost price, but he uses false weight instead of actual weight. Then,

       Gain %  = $\frac{Error}{\left (True\, Value\, -\, Error\right )}\times 100$


Example 1. :-  A boy buy a pen for Rs 25 and sells it for Rs 20. Find his loss per cent?
      Sol. 
                 Given -     CP = Rs 25
                                  SP = Rs 20
                     Then,    Loss = CP - SP
                                           = 25 - 20
                                           = Rs 5

         Loss %  = $\frac{Loss}{CP}\times 100$

                       = $\frac{5}{25}\times 100$

                       = 20 %

Example 2. :-  A book was sold for Rs 27.50 with a profit of 10 % . If it were sold for Rs 25.75, then waht would have been the percentage of profit or loss?
    Sol.
               SP = Rs 27.50
               profit = 10 %

           CP = Rs $\frac{100}{\left ( 100\, +\, Gain\% \right )}\times SP$

                 = Rs $\left ( \frac{100}{110}\times 27.50 \right )$

                 =Rs 25

When   SP = Rs 25.75
          profit = 25.75 - 25
                    = Rs 0.75

    $\therefore$   profit %  = $\left (\frac{profit}{CP}\times100\right )$

                          = $\left ( \frac{0.75}{25}\times 100 \right )$

                          = 3 %