Friday, 13 March 2015

16. GMAT Arithmetic Word Problems --- PROFIT AND LOSS Concept and Important Formulae

           PROFIT AND LOSS  -- IMPORTANT FORMULAE

This chapter is as much important as other chapters in the arithmetic section, since it is chapter of applications by which we calculate profit , loss , discount in day to day business.
When a person deals in the purchase and sale of any item, he either gains or loses some amount generally. In day to day life we sell and purchase things as per our requirement. A customer can get things in the following manner.
Manufacturer               -> Whole sale     ->     Retailer

Terminology:
Cost Price: The cost price of an article is the price at which an article has been purchased. It is abbreviated as C.P
If an article is purchased for some amount and there are some additional expenses on transportation, labour cost, commission or repair charges  etc. , these are to be added in the cost price. Such expenses are called overhead expenses or overhead costs.
Selling price: The selling of an article is the rpice at which an article has been sold . It is abbreviated as SP
Profit or gain: If the selling price of an item is more than the cost price, there is a profit or gain.
        Thus Profit or gain = Selling price – Cost price            SP > CP
Loss: If the cost price of an article is greater than that selling price, then there is a loss.
       Thus Loss = Cost price – Sell Price         CP > SP

Some Important Formulae :

            1)  Profit = SP – CP
Example: A merchant bought an article for Rs 1250 and sold for Rs 1400. What is the profit ?
Explanation: Cost price= Rs 1250  Selling price = Rs 1400
                 Profit = SP –CP = 1400 -1250=Rs  250

           2) Loss = CP –SP
Example: A person bought an article for Rs 1250 and sold for Rs 1175. What is the profit?
Explanation :  Cost price= Rs 1250  Selling price = Rs 1175
                 Loss = CP –SP = 1250 – 1175 = Rs 75

        3) Profit %  = $\frac{Profit\%}{100}$   x 100%
The cost price of a camera is Rs Rs 20000 and selling price is Rs  25000. Calculate profit percentage.
Solution:  We have CP = Rs 20000  and SP= Rs 25000
                    Profit = SP – CP = Rs 25000 –Rs 20000 = Rs 5000
                         Profit %  =
Profit / CP
  x 100%
                         Profit% =
5000 / 20000
   x 100% = 25%

         4)  Loss % = $\frac{loss\%}{100}$    x 100%
Sunil bought a gold ring for Rs 7500 and sold it for Rs 6750. Find his loss percentage ?
Solution : Here CP = Rs 7500  SP = Rs 6750    CP> SP  So there is loss.
                   Loss = CP – SP =  7500 – 6750 = Rs 750
                            Loss % =
Loss / CP
   x 100%
                                        
750 / 7500
   x 100% = 10%

        5) Profit = CP X$ \frac{Profit\%}{100} $
A man bought an article for Rs 2400 and sold at a profit of 10%. What is the profit in rupees ?
Explanation : CP = Rs 2400  Profit % = 10%
               Profit = CP x $ \frac{Profit\%}{100} $
                        = Rs 2400 x
10 / 100
= Rs  240

     6) Loss =  CP x
loss% / 100
Lakshmi bought an article for Rs 12000 and sold at a loss of 15%.What is his loss in rupees ?
Explanation : CP= Rs 12000    Loss % = 15
         Loss = CP x
loss% / 100
         Loss = Rs 12000 x
15 / 100
= Rs  1800
Note : Profit and loss are always calculated on the basis of cost price unless otherwise mentioned in the problem.

         7)  When an article is sold at a profit%, then Selling price
Selling price = Cost price x
(100+profit%) / 100
Example : Mr Shastri buys a washing machine for Rs 9000. For how much should he sell so that there is a gain of 8% ?
Explanation : We have CP= Rs 9000  Gain % = 8%
       Selling price = Cost price x
(100+profit%) / 100
                          = Rs 9000 x
(100+8) / 100
                          = Rs 9000 x
108 / 100
                          = Rs 9720

       8) When an article is sold at a loss%, then Selling price
Selling price = Cost price x
(100-loss%) / 100
Example : Mr Sudheer buys a camera for Rs 9000 and sold at a loss of 15%. Find the selling price?
Explanation : We have CP= Rs 9000  Loss % = 15%
       Selling price = Cost price x
(100-15%) / 100
                          = Rs 9000 x
                          = Rs 9000 x
85 / 100
                          = Rs 7650

       9)  When the selling price and gain % is given , then cost price is
                CP = SP  X  (
100 / (100+profit%)
)
Example: By selling an article for Rs 8400 ,  Kartik gains 20%. Find the cost price of the article?
Explanation : Here SP= Rs 8400  and Profit% = 20%
CP = SP  X  (
100 / (100+profit%)
)
           CP = Rs 8400 x 100/ 100+ 20
                = Rs 8400 x 100/120
                = Rs 7000

       10)  When selling price and loss% is given , then cost price is
             CP = SP  X  (
100 / (100- Loss%)
)
 Example: By selling an article for Rs 6400 ,  Soumya got a loss  of 20%. Find the cost price of the article?
Explanation : Here SP= Rs 6400  and Loss% = 20%
           CP = SP  X  (
100 / (100- Loss%)
)
           CP = Rs 6400 x
100 / (100-20)
                = Rs 6400 x
100 / 80
        = Rs 8000

Discounts :

Marked Price : Basically to avoid loss due to bargaining by customer and to get profit over the cost price , seller increases the cost price by a certain value .
This increase in value of over cost price is known as mark-up and the increased price is (Cost price + Mark up) marked by the seller is called marked price or printed price or list price.   This price is different from cost price and sale price.

           Marked Price = CP + Mark-up
           Marked Price = CP + (Percentage mark-up on CP)

The amount by which the seller marks up the cost price can be expressed as a percentage of the cost price. This percentage is called mark up percentage
 Mark- up percentage =
Increase in the price / Cost price
x 100 %
Generally, good are sold at marked price , if there is no further discount on the marked price. In this (no discounts are given on market price ), the selling price and marked price are equal.

Example : If the cost price of an article is Rs 600 and the percentage markup is 25%. What is the marked price ?
Explanation: MP = CP + (% markup on CP)
% markup on CP = 600 x
25 / 100
                        = Rs 150
                      Marked price = 600 + 150
                                          = Rs 750
Discount : The reduction made on the marked price of an article is called the discount
                Discount Percentage =
Discount / Marked Price
   x 100%

The marked price of an article is Rs 1200 and a cash discount of Rs.300 offered. What is the discount percentage?
Explanation :  Discount = Rs  300    Market price = Rs 1200
  Discount Percentage =
Discount / Marked Price
   x 100%
ð  Discount% = $\frac{300}{1200}$    X 100%
ð                    = 25%
When marked price and discount percentage is given, then selling price is
            SP = MP X
(100- Discount%) / 100

Example : Marked price of an article is Rs 6600 and the discount is 10%. Find the selling price ?
Explanation : Discount % = 10%     Marked Price = Rs 6600
 Selling price SP = Marked Price  x
(100- Discount%) / 100
                                     =  6600  x
(100-10) / 100
                                     = 6600 x
90 / 100
                                      = Rs 5940


For Solved Examples on Profit and Loss , Solved Problems on Profit and Loss 1


For more solved problems  ,  Profit and Loss Solved Example 2

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