Sunday, November 16, 2014

Profit and Loss

Import Concepts

Cost price: Cost price is the price at which the seller has acquired the article in question.

Selling Price: Selling price is the price at which the seller is willing to sell the product.

Profit: Profit is the amount the seller earns by selling an article at a price greater than the cost price.
                     
                Profit = Selling Price - Cost price

Loss: Loss is the amount the seller loses by selling an article at a price less than the cost price.
                Loss =  Cost price - Selling Price 

Profit Percentage: Profit percentage is the profit percent that the seller earns on the sell the article. It is calculated on the cost Price.

Overheads: overheads is the expenses that the seller has to incur to sell the products/articles. Overhead includes the rent of the shop, salaries of the employees, utilities bills, advertisement bill or any kind of expenses the seller has to pay to keep his business running.

Fixed Costs: Fixed cost is the cost that the seller has to bear in spite of quantity he is selling. Fixed cost include the rent , utility bills, employee salary and so

Variable Costs: Variable cost or direct cost is the cost the seller has to bear to sell the article. The cost price of the articles, cost price of the raw material and others.
 

Formula for profit and loss:

1.Profit Percentage =  {(S.P. - C.P)/C.P.}x100

2.Loss Percentage  =  {(C.P. - S.P.)/C.P.}x100

3.To find the Cost Price when Selling Price (S.P.) and Percentage profit (x) is given
                  Cost Price =   {S.P/(100 + x)} x 100

4.To find the Selling Price when the cost price (C.P.) and percentage profit (x) is   
   given by
                  Selling Price = {(100 + x)(C.P.)/100}                                                                    

5.To find the Cost Price when Selling Price (S.P.) and Percentage loss (x) is given
                  Cost Price =   {S.P/(100 - x)} x 100

6.To find the Selling Price when the cost price (C.P.) and percentage loss (x) is   
   given by
                  Selling Price = {(100 - x)(C.P.)/100}

7. If an article is sold at a profit of x% which is further sold at a profit of y% then 
    the final Selling price is 

                  Final Selling Price = Initial Cost Price{(100+x)/100}{(100+y)/100)  


8. If two successive profits x and y are made on the same article then the net 
    profit is 
                  (x + y + xy/100)   
    Note: above formula could also be used for loss. Just make sure to use +ve 
    sign for profit and -ve sign for the loss.  

9. If a false weight is used instead of the true weight then, the profit 
    percentage  is 
                         {(True Weight - false weight)/False Weight} x 100



                      

Solved Examples:

1. An article is sold for 75 at a loss of 25%. Then find the cost price of the article.

Solution:
 Using the formula 5 mentioned above we have ,
              Cost Price =   {S.P/(100 - x)} x 100
                             =   {75/(100 - 25)} x 100
                             =   {75/75}x 100
                             =   (1/1)x100
                             =    100

2. An article with a cost price of Rs. 840 is sold for a profit of 10% and then 
   again sold for a profit of 20%. Find the final selling price.

Solution:
Using the formula 7 mentioned above, we have 
           Final Selling price = 840{(100+10)/100}{(100+20)/100}
                                    = 840(110/100)(120/100)         
                                    = 840(11/10)(12/10)
                                    = 840(1.1)(1.2)
                                    = 1108.80

3. A sells a mobile to B worth Rs. 10,000. He makes a profit of 15%. Again B 
   sold it back to A at a loss of 15%. Find the A's profit or loss.

Solution:
Using the formula 8, taking Y as negative, We have
Net profit/loss  = ( 15 - 15 -225/100)
                      = (-2.25)
 First, A made a profit of 15% and again total loss of  (-2.25)% in the entire deal was profit to A.
Therefore, total Profit A made = 15+2.25 = 17.25 %




4. I gain 0.70 paisa on Rs. 70. My gain percent is : 
(a)0.1%                         (b)1%
(c)7%                            (d) 10% 

Solution:

Total profit = 0.70 paisa
And C.P. = Rs 70
Therefore, Gain percent = (0.70/70)x100 = 1%


 5. In terms of percentage profit , which is the best transaction ? 
C.P (in Rs.)                                  profit (in Rs.)
(a)36                                              17
(b)50                                              24
(c)40                                             19 
(d) 60                                             29 

Solution:
We have to calculate the percentage profit in each case, the table becomes


C.P (in Rs.)                                  profit (in Rs.)   profit %
(a)36                                              17                 47.22
(b)50                                              24                 48
(c)40                                              19                 47.5
(d) 60                                             29                 48.33

Therefore, the best transaction is (d)

6. A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent ?
(a) 4(1/6) %                                (b)6(1/4)
(c)8(1/3)%                                   (d)20%

Solution:
Rate per kg at which the potatoes are bought = 420/70 = Rs 6 per kg
And they are sold at 6.5 kg per kg.
Therefore total profit = (0.5/6)x100 = 8(1/3) %

7. The price of the a radio is raised by 40% above the cost price and sold at a discount of 10%. What will be percentage of profit?
 (a) 14%     (b)  30%
 (c) 25%     (d)  26%

Answer:  (d)  26%
Solution:
Let the Cost price was 100 then the selling price at 40% profit will be 140. 
And at this price a discount of 10% is offered then the final selling price will be  
         140 - (0.10)(140) = 140 - 14 = 126
And net profit is   126 - 100 = 26 and in percentage it will be 26%

8. Profit after selling a commodity for 425 is the same as the loss after selling it for 355.The cost of the commodity is 
(a) 390      (b) 395
(c) 400      (d)  385

Answer:(a) 390
Solution:
Since the profit after selling the commodity at 425 and loss after selling it at 355 is the same.Then the Cost Price for the commodity lies exactly in the middle of the two numbers. It will be found by finding the averages of the these two numbers.
    There the Cost Price   = (425 + 355)/2 = 390

9. A watch is purchased for 400 and sold for 460.The profit percentage is 
   (a) 15.5%        (b) 12%
   (c) 13%           (d)  15%

Answer:
Solution:
Total profit = 60 and cost price is 400. Therefore the percentage profit is 
(60/400)x100 = 15 %

10. By selling an article for 450 , a man loses 10%. The gain or loss percent if he sells it for 540 is
(a) gain 9%   (b)  loss 9%
(c) gain 8%   (d)  loss 8%

Answer: (a) gain 9%
Solution:
Here, Cost  Price = 450(110/100) = 495
         If he sold it for 540, the profit would have been (540 -495) =     45
         And therefore the profit = {(45)/(495)} x100 =  9%      

11. The cost price : selling price of an article is a : b. If b is 200% of a then the percentage of profit on  cost price is
(a) 75%    (b) 125%
(c) 100%   (d) 200%


Answer:(c) 100%  
Solution:
Given that b is 200% of a. This implies that if a = 1 then b = 2. 
This Implies cost price : Selling price = 1:2
And profit percentage = {(2-1)/1}x 100 = 100%  

12. The successive discounts of 10% and 20% are equivalent to a single discount of 
(a) 30%           (b) 28%
(c) 25%          (d) 27%


Answer:   (b) 28%
Solution:
Let the Selling price be 100. Then the discount of 10% is 10. The selling price
will become 90. Again a 20% discount is offered then the selling price becomes 90 - (0.2)(90) =  72.
Hence the net discount becomes 100 - 72 = 28% 

13. A dealer marks his goods at 40% above the cost price and allows a discount of 20% on the marked price. The dealer has a
(a) loss of 20% (b) gain of 25%
(c) loss of 12% (d) gain of 12% 


Answer:(d) gain of 12%
Solution:
Let the Cost price be 100. Then after it was marked up 40% , the selling price would be 100 + (0.40)(100) = 140.
Again a discount of 20% was offered on the marked price then the final selling price become
                          140 - (0.20)(140) = 140 - 28 = 112
And the profit is 112 - 100 = 12% or gain of 12%

14. A person sells 400 mangoes at the cost price of 320 mangoes. His percentage of loss is 
 (a) 10    (b) 15
 (c) 20    (d) 25


Answer: (c) 20 % 
Solution:
Out of 400 mangoes he sold,he was able to recover the cost price of 320 mangoes. And his lost is the cost price of the 80 mangoes.
Thus, total loss = {(80)/400} x 100 = 20 %

15. A shoe company sold 50 pairs of shoes on a day costing Rs. 189.50 each 
for Rs. 10,000. Then the profit obtained in rupees is
(a) 522        (b) 525
(c) 573        (d) 612

Answer:
Solution:
Cost of 50 pairs of shoes = (189.5)(50)  = 9475
And he sold them for     10000
Therefore , total profit =  10000 - 9475
                                 =  525

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