November 17, 2016

Profit, Loss and Discount - Concepts


Quantitative Aptitude for IBPS PO & Clerk


Concepts:

  1. Cost Price: Price at which the article is purchased
  2. Selling Price: The price at which the article is sold

Formulas:


1. PROFIT P

  • = Selling Price(SP) - Cost Price (CP)
  • P = SP - CP

2. LOSS L

  • = Cost price - Selling price
  • L = CP - SP

3. PROFIT PERCENTAGE P%

  • = (Profit / CP) × 100
  • P% = [(SP ÷ CP) - 1] × 100
    • we get this by substituting P = SP - CP

4. LOSS PERCENTAGE L%

  • = ( Loss / CP ) × 100
  • L% = [1 - ( SP ÷ CP )] × 100
    • We get this by substituting L = CP - SP

5. Finding SP when CP and P% or L% is given

  • If Profit % is given, then
    • SP = [( 100 + P% ) × CP] ÷ 100
    • This can also be written as
      • SP = CP × [( P% ÷ 100 ) + 1 ]
      • which is again written as 
      • SP = CP × [( P% + 100 ) ÷ 100 ]
  • When Loss % is given
    • SP = [( 100 - L% ) × CP] ÷ 100
    • This can also be written as
      • SP = CP × [( L% ÷ 100 ) - 1 ]
Quantitative Aptitude for IBPS PO, Clerk mains, SBI, RBI Assistant, LIC AAO Exams
      • which is again written as 
      • SP = CP × [( L% - 100 ) ÷ 100 ]

6. Finding CP when SP and P% or L% is given

  • When Profit percentage is given
    • CP = ( 100 × SP ) ÷ ( 100 + P% )
    • This can also be written as
      • CP = [100 ÷ ( 100 + P% ) × SP
  • When Loss % is given
    • CP = ( 100 × SP ) ÷ ( 100 - L% )
    • This can also be written as
      • CP = [100 ÷ ( 100 - L%) × SP

7. When Marked price is MP, Discount % = d%, then

  • SP = [ MP × ( 100 - d% ) ÷ 100]
  • MP = [ 100 × SP ] ÷ [ 100 - d% ]

8. We have

  • CP + Profit = SP; SP - Discount = MP

9. When 2 articles are sold, each at ₹ x

  • of which one article got P% profit
  • other got P% loss
  • Then there will be 
    • an overall loss
    • therefore, L% = P² / 100 %
    • Loss in rupees = 2P² X / ( 100² - P² )

10. When 2 articles has the same cost prics, ₹ x

  • of which one article got P% profit
  • other got P% loss
  • Then there will be 
    • No loss No Profit

11. Finding Single Discount Rate SDR, when two successive discounts are given on an article

  • let the successive discounts be d₁% and d₂%
  • then
  • SDR = 100 - d₁% × d₂% × 100
Treat DISCOUNT as LOSS always
  • so we have
  • SDR = 100 - [( 100 - d₁ ) / 100] × [( 100 - d₂ ) / 100] × 100

12. What should be the Marked Price MP on an article with discount y%, to get a profit of x%?

  • we have 
    • discount = y% ⇒ loss %; 
    • and profit % = x%
  • to get the Marked price
  • MP = ( P% / L% ) × 100
  • = [(100 + P) / 100  ] / [( 100 - L) / 100 ] × 100
  •  MP = (100 + P) / ( 100 - L) × 100
  •  (100 + x ) / ( 100 - y ) × 100

13. If the cost Price of 'A' articles is equal to the Selling price of 'B' articles, if A > B, then there will be profit

  • P% = ( A - B ) / B × 100
  • A = CP of A articles
  • B = SP of B articles

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