PROFIT AND LOSS

INTRODUCTION-
                                 Let's go through a small story to understand all (most😛😛) the terminologies and concepts related to PROFIT-LOSS.

Honey( a fashion freak) goes to a local shop to buy a T-shirt. The price of the T-shirt is Rs.500. After an altercation with the shopkeeper, Honey was able to buy that T-shirt for Rs.400. Although shopkeeper reduced the price he was able to save Rs.100 by selling that T-shirt to Honey.

TERMINOLOGIES AND CONCEPTS-

1)Selling Price= Rs.400
   The price at which an article is sold.

2)Cost Price = Rs.300
   The actual price of the article.

3)Marked Price(Tag Price) = Rs.500
   The price increased by shopkeepers to earn an extra profit is known as MARK UP(Rs.100 in this case).

4)Profit = Rs.100
   Any extra money that the seller gets while selling i.e;
  From Cost price to Selling Price;
  Selling Price - Cost Price = Profit

5)Loss = Any extra money that seller loses while selling like selling an article that costs him Rs100 for Rs50
Loss = Cost Price - Selling Price

6) Profit% = (Profit *100)/CP %

7) Loss% = (Loss*100)/CP %

8) Discount = Rs.100
    Discount = Marked Price - Selling Price

Let's go through some examples for better understanding.

EXAMPLE 1-
A man buys a shirt and a trouser for Rs.371. If the trouser costs 12% more than the shirt,
find the cost of the shirt.

SOLUTION-

It is given that touser cost is 12% more than the shirt,
Let the shirt cost = Rs.x
Trouser cost = Rs. 1.12x
Now we know that total cost of these two items is Rs.371
i.e; x+1.12x=371
      x=371/2.12 =175(used calculator😛)

Now,
12% = 12/100 =3/25
Let the cost of shirt = 25 units
Cost of trouser = 25+3=28 units
Total cost= 25+28=53 units
Now, 53 units= Rs.371
          1 unit = 371/53 = Rs.7
Cost of shirt = 25units = 25*7 = Rs.175 ANS

EXAMPLE 2-
By selling 15 mangoes, a fruit vendor recovers the cost price of 20 mangoes. Find the
profit percentage.

SOLUTION-                       For this type of questions, we have a direct formula,

                      PROFIT% = GOODS LEFT*100/ GOODS SOLD
                     Profit%=5/15 *100 = 100/3 %

BUT,
 Let the cost of one mango = Re 1
Cost of 20 mangoes = Rs. 20
In this case, CP of 15 mangoes =Rs 15
 SP of 15 mangoes = RS20

SP= CP(1+Profit/100)
20=15(1+Profit/100)
4/3 = 1+ Profit/100
Profit%=100/3 ANS


EXAMPLE 3-
A dishonest businessman professes to sell his articles at cost price but he uses false weights with which he cheats by 10% while buying and by 10% while selling. Find his percentage profit.

METHOD 1-
Let total weight =1000 gms
While buying,
he buys 1100 instead of 1000 gms
while selling he sells 900 gms instead of 1000 gms
Total Profit = 100+100 =200gms
Profit % = 200/900 * 100% = 200/9% ANS

METHOD 2-
While buying he cheats by 10% = 10/100 =1/10
i.e; instead of 10units he gets 11units
similarly while selling, he sells 9units instead of 10unit

Now we know,
SP=CP(1+Profit/100)
10/9 = 10/11 (1+x/100)
11/9= 1+x/100
x= 2*100/9 = 200/9%ANS

EXAMPLE 4-
A man sells three articles, one at a loss of 10%, another at a profit of 20% and the third one at a loss of 25%. If the selling price of all the three is the same, find by how much percent is their average CP lower than or higher than their SP.

SOLUTION-
Article 1 = 10% loss = 10/100= 1/10
i.e; CP=10  SP=9
Similarly for article 2, CP = 5   SP= 6
For article 3, CP=4    SP =3
Now Sp is same for all the three articles,
LCM(9,6,3) = 18

                               CP                   SP

ARTICLE 1          20                     18

ARTICLE 2          15                     18

ARTICLE 3          24                     18

Now average CP= (20+15+24)/3 = 59/3
Average Sp = (18+18+18)/3 =54/3
%age achange = (Avg CP - Avg SP)/Avg Sp *100%
                         = (59/3 - 54/3)/54/3 *100%
                         =5/54 *100%
                         =9.265% higher ANS



EXAMPLE 5-
A man sells a TV set for Rs.3450 and makes a profit of 15%. He sells another TV at a loss of 10%.
If on the whole, he neither gains nor loses, find the selling price of the second TV set.

SOLUTION- Profit % =15% = 15/100 = 3/20
If CP = 20 units
SP =20+3 = 23units
Now 23 units = 3450
         1 unit= 3450/23 = 150
         3 units=450

Now for second TV,Loss%= 10% = 10/100 =1/10
CP = 10 units
SP = 10-1= 9 units

Now 1 unit loss in the second case must be equal to 3 units gain in first case
i.e; 1unit=Rs.450
So SP of Second TV = 450*9 = Rs.4050 ANS



EXAMPLE 6-
A manufacturer estimates that on inspection 12% of the articles he produces will be rejected. He
accepts an order to supply 22,000 articles at Rs.7.50 each. He estimates the profit on his outlay
including the manufacturing of rejected articles, to be 20%. Find the cost of manufacturing each
article.

SOLUTION-

12% rejected = 12/100 = 3/25
So out of 25 articles, only 22 will be selected.
Now for supplying 22,000 articles, he must manufacture 25,000 articles.

NOw we know
SP= CP(1+Profit/100)
22000*7.50 = 25000*x(1+20/100)

Solving this we get x=Rs.5.50 ANS





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