This document defines key terms related to profit and loss such as cost price, selling price, profit, loss, marked price, and discount. It also provides formulas to calculate profit/loss percentage, selling price given cost price and profit/loss percentage, cost price given selling price and profit/loss percentage, discount amount and percentage. Important notes state that selling price is 112% of cost price for 12% gain and 80% of cost price for 20% loss. Sample problems demonstrate applying the formulas and concepts to calculate profit percentage in different scenarios.

3. TERMS -
• Cost price – the price at which a product is
purchased, is called cost price. (C.P.)
• Selling price – the price at which a product is sold, is
called selling price.(S.P.)
• Profit – it occurs when the selling price is more than
cost price. (P)
S.P. > C.P.
• Loss – it occurs when the selling price is less than
cost price. (L)
S.P. < C.P.
• Marked price – the price on the label of a product, is
called marked price or list price (M.P.)
• Discount – the reduction in price offered on the
marked price. (D)

5. FORMULAS -
•Profit/ gain = S.P. – C.P.
•Loss = C.P. – S.P.
•Gain% =
Gain ×100
C.P.
•Loss % =
Loss ×100
C.P.

6. FORMULAS -
•S.P. (in gain) =
100 + Gain %
100
× C. P.
•S.P. (in loss) =
100 − Loss %
100
× C. P.
•C.P. (in gain) =
100
100 + Gain%
× S. P.
•C.P. (in loss) =
100
100 −L𝑜𝑠𝑠%
× S. P.

7. FORMULAS -
• Discount = M.P. – Rate of discount
• S.P. = M.P. – Discount
•Discount % =
Discount
M.P.
× 100

8. IMPORTANT NOTES –
• If a product is sold at certain gain (i.e. 12%),
then S.P. = 112% of C.P.
• If a product is sold at a certain loss (i.e. 20%),
then S.P. = 80% of C.P.
• If a trader sell his goods at C.P. but uses false
weight then Gain% =
Error
True value −Error
× 100

10. Q 1. A dishonest shopkeeper sells sugar at ₹ 18/kg which he has
bought at ₹ 15/kg and he is giving 800 gm instead of 1000 gm.
Find the actual profit percentage.
Sol. Given :- C.P. = 15/kg; S.P. = 18/kg
So profit made by shopkeeper =
Profit/ gain = S.P. – C.P.
Profit = ₹18 – ₹15 = ₹ 3
Gain% =
Gain ×100
C.P.
Gain% =
3 ×100
15
= 20%

11. CONTINUE…..
This will be the profit if actually sold 1kg sugar.
But here the profit = Gain% =
Error
True value −Error
× 100
Gain% =
200
1000 −200
× 100 =
200
800
× 100 = 25%
Q 2. If the C.P. of 12 pens is equal to S.P. of 8 pens, the
gain percent is ?
Sol. Suppose C.P. of 1 pen = ₹ 1
Then C.P. of 8 pen = ₹ 8
S.P. of 8 pen = ₹ 12
Then Gain = S.P. – C.P. = ₹12 – ₹8 = ₹4

12. CONTINUE…….
Then Gain % =
Gain ×100
C.P.
Gain % =
4 ×100
8
= 50%
Q 3. The cost price of 20 articles is the same as selling price of x
articles. If the profit is 25%, find out the value of x.
Sol. Suppose of C.P. of 1 article = ₹ 1
C.P. of x articles = ₹ x
S.P. of x articles =₹ 20
Profit % = =
(S.P.− C.P.)×100
C.P.
=

13. CONTINUE…….
= 25 =
(20 −X)×100
X
= ¼ =
(20 −X)
X
= X = 4(20 –x)
= X = 80 – 4x
= X + 4x = 80
= 5x = 80
= X = 80/5
= X = 16