06 December, 2015

Profit and Loss Formulas, Shortcuts and Problems

Aptitude Profit and Loss Basics

Basic Points to Remember:

  • Cost Price: The price, at which an item is purchased, is called it's Cost Price and is denoted by C.P.
  • Selling Price: The price, at which an item is sold, is called it's Selling Price and is denoted by S.P.
  • Profit [or] Gain: If S.P is greater than C.P, then it is called as Profit.
  • Loss: If C.P is greater than S.P, then it is called as Loss.
  • Market Price [or] Label Price: Retailer or Seller marks the price on a label and attaches it to the items or articles.
  • Discount: Reduction in the Marked price or Market price or Label price is called Discount.

Important Formulas:

  1. Profit [or] Gain = (Selling Price) - (Cost Price)
  2. Loss = (Cost Price) - (Selling Price)
  3. Gain Percentage = (Gain/Cost Price)*100
  4. Loss Percentage = (Loss/Cost Price)*100
  5. Selling Price = [(100 + Gain %)/100]* C.P
  6. Selling Price = [(100 - Loss %)/100]* C.P
  7. Cost Price = [100/(100 + Gain %)]* S.P
  8. Cost Price = [100/(100 - Loss %)]* S.P
  9. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss = (x)2/100 
  10. If a grocer sells its goods at cost price, but uses a false weight instead of true weight. Then
    Percentage Gain = [(True Weight - False Weight)/False Weight]*100
Profit and Loss Problems:
1. A man purchased a book for Rs. 300 and sold it out for Rs. 390. What is the gain or loss percentage?
A) 15 %                 B) 20 %                   C) 25 %                 D) 30 %


Ans. D
Solution:
Gain % = [(390 - 300)/300] * 100
Gain % = 90/3
Gain % = 30 %.

2. A Man purchased a table for Rs. 1600 and sold it for Rs. 1280. What is gain or loss percentage?
A) 10 %                 B) 20 %                   C) 22 %                 D) 25 %


Ans. B
Solution:
Loss % = [(1600 - 1280)/1600] * 100
Loss % = 320/16
Loss % = 20 %.

3. A Man sold  a car for Rs. 2600, there by he gained 30 %. Then find out the C.P ?
A) Rs. 1,800          B) Rs. 1,900              C) Rs. 2,000        D) Rs. 2,100


Ans. C
Solution:
C.P = [100/(100 + Gain %)]*S.P
C.P = [100/(100 + 30)]*2600
C.P = [100/130]*2600
C.P = 100*20
C.P = Rs. 2,000

     [OR]      
Short Cut Method:
2,600 ==> 130 %
? ==> 100 %
X = [100/130]*2600
X = Rs. 2,000.

4. A Man sold two horses for Rs. 1,000 each and he gained 10 % on one horse and 10 % loss on other. Then find out total gain or loss ?
A) 0.5 %              B) 1 %                         C) 1.5 %             D) 2 %


Ans. B
Solution:
Refer Formula No. 9 in above Formulae
% Loss = (10)2/100
% Loss = 100/100
% Loss = 1 %.

5. A dishonest dealer professes to sell his goods at C.P but he use a weight of 800 gms instead of 1 Kg. Then what is gain or loss percentage ?
A) 10 %              B) 15 %                        C) 20 %              D) 25 %


Ans. D
Solution:
Refer Formula No. 10 in above Formule
% Gain = [(1000 - 800)/800]*100
% Gain = 200/8
% Gain = 25 %.

6. A Man sold an article for Rs. 21,000. There by he loss 30 %. What is the C.P ?
A) Rs. 25,000           B) Rs. 28,000           C) 30,000          D) 32,000


Ans. C
Solution:
C.P = [100/(100 - Loss %)]*S.P
C.P = [100/(100 - 30)]*21,000
C.P = [100/70]*21,000
C.P = 100*300
C.P = Rs. 30,000

     [OR]      
Short Cut Method:
21,000 ==> 70 %
? ==> 100 %
X = [100/70]*21,000
X = Rs. 30,000.

7. I gain 70 paise on Rs. 70. What is my gain percent ?
A) 0.1 %                  B) 1 %                        C) 7 %                       D) 10 %


Ans. B
Solution:
% Gain = (0.70/70)*100
% Gain = 70/70
% Gain = 1 %.

Points to Remember:

In a given problem only Articles or Quantities are given, then use the following formulae.
  1. Profit = (Cost Quantity) - (Selling Quantity)
  2. Loss = (Selling Quantity) - (Cost Quantity)
  3. % Gain = (Profit/Selling Quantity)*100
  4. % Loss = (Loss/Selling Quantity)*100

Example Problems:

8. The C.P of 15 articles is equals to the selling price of 12 articles. Then find the Profit or Loss percentage?
A) 20 %                   B) 25 %                      C) 28 %                     D) 30 %


Ans. B
Solution:
% Gain = (Profit/S.Q)*100 = [(C.Q - S.Q)/S.Q]*100
% Gain = [(15 - 12)/12]*100
% Gain = (3/12)*100
% Gain = 25 %.

9. A Man purchased 11 articles for Rs. 10 and he sold out 10 articles for Rs. 11. What is the gain or loss percentage ?
A) 10 %                  B) 11 %                       C) 20 %                     D) 21 %


Ans. D
Solution:

  Articles          Books
    a = 11   ==>    b = 10
    c = 10   ==>    d = 11
% Gain = [(ad - dc)/bc]*100
% Gain = [(121 - 100)/100]*100
% Gain = (21/100)*100
% Gain = 21 %

10. The cost price of 19 articles is equal to the selling price of 16 articles. What is the Gain percentage ?
A) 60/17 %            B) 300/19 %                C) 75/4 %                   D) 20 %


Ans. C
Solution:
% Gain = (Profit/S.Q)*100 = [(C.Q - S.Q)/S.Q]*100
% Gain = [(19 - 16)/16]*100
% Gain = (3/16)*100
% Gain = (3/4)*25
% Gain = 75/4%.

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