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 ]
• 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