Basic Definitions and Formulas
Cost price (C.P.) : This is the price at which an article is purchased.
Selling price(S.P.) : The price at which an article is sold, is called its selling price,
Profit or Gain : If S.P. is greater than C.P. , the seller is said to have a profit or gain.
Loss : If S.P. is less than C.P., the seller is said to have incurred a loss.
· Profit or Loss is always calculated on the cost price.
· Marked price: This is the price marked as the selling price on an article, also known as the listed price.
· Discount or Rebate: This is the reduction in price offered on the marked or listed price.
Below is the list of some basic formulas used in solving questions on profit and loss:
1. Gain = (S.P.) – (C.P.)
2. Loss = (C.P) – (S.P.)
3. Loss or gain is always reckoned on C.P.
4. Gain% = (Gain X 100/C.P)
5 Loss% = (Loss X 100/C.P)
6. S.P. = (100 + Gain%)/100 × C.P.
7. S.P. = (100 + Loss%)/100 × C.P.
8. C.P. = 100/(100 + Gain%) × S.P.
9. C.P. = 100/(100 - Loss%) × S.P.
10. If an article is sold at a gain of say, 35%, then S.P. = 135% of C.P.
11. If an article is sold at a loss of say, 35%, then S.P. = 65% of C.P.
12. 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 given by :
Loss% = (common Loss Gain%/10)2 = (x/10)2
13. If a trader professes to sell his goods at cost price, but uses false weights, then
Gain% = [Error/ (True value) - (Error) X 100]%