1) The document provides information on profit and loss calculations including formulas for cost price, selling price, trade discount, cash discount, and calculating percentage profit and loss. 2) Various examples are given for calculating profit/loss percentage when cost price and selling price are given, finding selling price when cost price and profit/loss percentage are given, and other profit/loss scenarios. 3) Step-by-step solutions are shown for examples involving finding cost price, selling price, profit/loss percentage in various circumstances. Formulas are provided for calculating marked price based on cost price, profit percentage and discount percentage.

1. Profit and Loss
KES’s
PRATIBHA COLLEGE OF COMMERCE AND COMPUTER STUDIES, PUNE
Mr. Kakde Santosh D.
Asst. Professor,
Department of Mathematics,
PCCCS, Pune-19
Maharashtra-India

2. In this Unit, we are learn:
1.
2.
3.
Terms and Formulae
Trade Discount and Cash Discount
Introduction to Commission and Brokerage

3. Terms and Formulae
1.
Cost Price (C.P.) :
The total amount paid for purchasing an article, transport charges, octroi etc. is called cost price of that article
Marked Price (M.P.) :
The price of an article which is printed in the price list or catalogue so as to ensure that the consumer
gets the article at that price is called marked price or list price or catalogue price .
Selling Price (S.P.) :
Total amount realised by selling an article is called selling price of that article.

4. 2. Trade Discount and Cash Discount
Traders who buy goods in large quantities from manufacturers or wholesaler are generally given
an allowance on the list price of the goods. This is known as trade discount.
The discount given by retailer to a purchaser is called cash discount.
Sometimes, a buyer may get benefit of both discounts. In such a case, cash discount should be
calculated on the net value
of the goods after deducting trade discount.
Thus, net selling price is the amount realised by the seller after giving discount. If no discount is
given, then S.P. will be same a the M.P.
If S.P. is more than the C.P. then we say that a profit is realised in the transaction.
Profit=S.P.-C.P.
If C.P. is more than the S.P. then we say that a loss is incurred in the transaction.
Loss=C.P.-S.P.

5. While solving the problems, students are advised to remember the following points:
1.
2.
3.
Percentage profit or loss is always calculated on the C.P.
Percentage profit or loss does not depend on number of articles sold (or purchased.)
Commission or discount is always given on S.P.
Note:If an article costing ₹ 𝑥 is sold at 𝑦% profit, its 𝑆. 𝑃. =
100 + 𝑦
100
𝑥
𝑆. 𝑃. =
100 − 𝑦
100
𝑥
and if it is sold at 𝑦% loss, then its

6. Examples:
𝑥 =
100
12000
X 1600
Type 1: To find percent profit / loss when S.P. and C.P. are given .
Example 1: A scooter costing ₹ 12,000 was sold for ₹ 10,400 after two years. Find the percentage loss.
Solution: Loss = ₹ 12,000 − ₹ 10,400 = ₹ 1,600
On C.P.₹ 12,000 loss ₹ 1,600
∴ On C.P. ₹ 100, loss ₹ 𝑥
∴ There is
40
3
% loss
𝒙 =
𝟒𝟎
𝟑

7. Type 2: To find S.P. when C.P. and percent profit/ loss is given.
Example: Goods worth ₹ 𝟔𝟎𝟎𝟎 are purchased. What should be the S.P. to earn a profit of 𝟏𝟐% ?
Solution:
𝑥 =
600
100
X 112
To earn 12% profit, an article costing ₹ 100 should be sold for ₹ 112. Thus,
When C.P. ₹ 100 , S.P. is ₹ 112
∴ When C.P. ₹ 6000 , S.P. is ₹ 6720
When C.P. ₹ 600, S.P. is ₹ 𝑥
∴
𝑥 = ₹ 6720
Goods should be sold for ₹ 6720
∴

8. Type 3:To find C.P. when S.P. and percent profit/ loss is given
Example: A camera when sold for ₹ 𝟏𝟔𝟕𝟒 resulted in a loss of 7%. What was the C.P. of the camera ?
Solution: A loss of 7% means if the camera was purchased for ₹ 100, it is sold for ₹ 63.
Thus,
When S.P. ₹ 93 , C.P. is ₹ 100
When S.P. ₹ 1674 , C.P. is ₹ 1800
∴
∴
When S.P. ₹ 1674 , C.P. is ₹ 𝑥
𝑥 =
1674
93
X 100
𝑥 = ₹ 6720
C.P. of the camera was ₹ 1800

9. Type 4:To find percent profit/ loss when some goods are sold at profit and remaining at loss.
Example: A book-seller purchased 𝟖𝟎𝟎 copies of a book for ₹ 𝟒𝟒𝟎𝟎. He sold 𝟔𝟎𝟎 at a profit of 𝟐𝟎% and remaining
copies at a loss of 𝟐𝟓%. Find percent profit/ loss in the total transaction.
Solution: Since C.P. of 800 copies is ₹ 4400 each copy cots ₹ 5.50
C.P. of 600 copies is ₹ (600 X 5.50) = ₹ 3300
S.P. of these copies at 20% profit = ₹ 100 +
20
100
X 3300
= ₹
6
5
X 3300
= ₹ (6 X 660)
= ₹ 3960
C.P. of remaining 200 copies = ₹ (200 X 5.50)
= ₹ 1100
These copies are sold at a loss of 25%

10. ∴ S.P. = ₹
100 − 25
100
X 1100
= ₹
3
4
X 1100
= ₹ 825
∴
∴
∴
Total S.P. = ₹ (3960 + 825)
= ₹ 4785
Profit = S.P. −C.P.
= ₹ (4785 − 4400)
= ₹ 385
When C.P. is ₹ 4400 , profit ₹ 385
When C.P. is ₹ 100 , profit ₹ 𝑥
𝑥 =
100
4400
X 385
𝑥 = 8.75
When C.P. is ₹ 100 , profit ₹ 8.75
∴ There is 8.75% profit in the total truncation.

11. Type 5:To decide the marked price of an article when C.P., percent profit and percent commission is known.
Example: A dealer in furniture buys chairs at ₹ 𝟑𝟒𝟎 each. At what price should he mark them for sale, so that he my earn
a profit of 𝟐𝟓% after giving 𝟏𝟓% discount ?
Solution: Let the marked price of a chair be ₹ 𝑥
∴ Discount at 15% =
15𝑥
100
∴ Net S.P. = 𝑥 −
15𝑥
100
=
85𝑥
100
=
17𝑥
20
The chair costs ₹ 340 and 25% profit is to be realised.
∴
∴ Net S.P.= ₹
100 + 25
100
X 340
= ₹
5
4
X 340
= ₹ 425
Thus, 17𝑥
20
= 425
𝑥 = ₹ 425 X
20
17
𝑥 = ₹ 500
Marked price of the chair should be ₹ 500
∴

12. Note: In this problem, we have seen how to find the M.P. of an article when the following are known:
𝑎
𝑏
𝑐 % discount to be given.
% profit to be realised.
However, We give below an elegant formula to find M.P. at once:
C.P. of the article.
M. P. =
100 + % 𝑝𝑟𝑜𝑓𝑖𝑡
100 − % 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡
X 𝐶. 𝑃.
Thus in the above problem,
M. P. =
100 + 25
100 − 15
X 340
=
125
85
X 340
= 125 X 4
M.P. = 𝟓𝟎𝟎

13. Type 6: Miscellaneous
Example: The profit realised by selling an article at ₹ 𝟒𝟗. 𝟓𝟎 is
𝟕
𝟒
times the profit realised by selling it at ₹ 𝟒𝟓. Find the
C.P. of the article.
Solution:Let the C.P. of the article be ₹ 𝑥
∴
∴
∴
∴
∴
∴
Profit when it is sold at ₹ 45 = ₹(45 − 𝑥)
Profit when it is sold at ₹ 49.50 = ₹(49.50 − 𝑥)
By given information, 49.50 − 𝑥 =
7
4
(45 − 𝑥)
198 − 4𝑥 = 315 − 7𝑥
3𝑥 = 315 − 198
𝑥 = 117
𝑥 = 39
C.P. of the article ₹ is 39

14. Example:
𝟏
𝟏𝟕
𝒕𝒉
of the cost price is
𝟏
𝟐𝟐
of S.P. 𝟏𝟎% of the C.P. and 𝟓% of the S.P. differ by 12. Find the C.P. and S.P.
Solution: Let 𝑥 be the C.P. and 𝑦 be the S.P. of article.
∴
𝑥
17
=
𝑦
22
𝑖. 𝑒. 22𝑥 = 17𝑦
Also,
𝑥
10
=
𝑦
20
+ 12 (Why ? )
… … … … … … … … … … … (𝑖𝑖)
… … … … … … … … … … … (𝑖)
∴ 2𝑥 = 𝑦 + 240
From 𝑖 and (𝑖𝑖)
22𝑥 − 17𝑦 = 0
22𝑥 − 11𝑦 = 240 X 11
and
Subtracting,
𝑦 = 440
∴
6𝑦 = 240 X 11
Subtractin in equation 𝑖𝑖
𝑥 = 340
Let₹ 340 be the C.P. and ₹ 440 be the S.P. of article.

15. Example: A man sold two machines at ₹ 𝟗𝟗𝟎 each. On one, he gained 𝟏𝟎% and on the other, he lost 𝟏𝟎%.Find
percentage profit or loss in the total transaction.
Solution: Let 𝑥 the C.P. of the machine on which he gained 10% be ₹ 𝑥
S. 𝑃. =
100 + 10
100
(𝐶. 𝑃. ) =
11𝑥
10
11𝑥
10
= 990
∴ 𝑥 = 900
Let the C.P. of the machine on which he lost 10% be ₹ 𝑦
∴ 𝑦 = 1100
By formula,
By formula,
S. 𝑃. =
100 − 10
100
(𝐶. 𝑃. ) =
9𝑦
10
9𝑦
10
= 990

16. Total C.P. = ₹ 900 + 1100 = ₹ 2000
Total S.P. = ₹ 2 900 = ₹ 1,980
Loss= ₹ 20
For C.P. of ₹ 2000, loss ₹ 20
For C.P. of ₹ 100, loss ₹ 1
Thus there is 1% loss in the total transaction.
∴
∴
∴

17. Home-Work
1.
2.
A piano is sold for ₹ 42,500 at a loss of 15% . For how much should it have been sold to earn a profit of 15%?
60 litters of diesel is bought at ₹ 8 per litter. If 10% is lost in transit, at what rate should the remainder
be sold to earn 10% on the whole?

18. Thank You