Government of TamilNadu

Department of Employment and Training

Course : Airmen Exam

Subject : Mathematics
Topic : Profit and Loss

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Department of Employment and Training.
 Profit and Loss

Basic Concepts

Let us learn profit and loss concepts in maths. It is well explained in terms of cost
price and selling price.
Profit(P)

The amount gained by selling a product with more than its cost price.

Loss(L)

The amount, the seller incurs after selling the product less than its cost price, is
mentioned as a loss.
Cost Price (CP)

The amount paid for a product or commodity to purchase it is called a cost price.
Also, denoted as CP. This cost price is further classified into two different
categories:

• Fixed Cost: The fixed cost is constant, it doesn’t vary under any
circumstances

• Variable Cost: It could vary depending as per the number of units

Selling Price (SP)

The amount for which the product is sold is called Selling Price. It is usually
denoted as SP. Also, sometimes called a sale price.

Marked Price Formula (MP)

This is basically labeled by Shopkeepers to offer a discount to the customers in

such a way that,

• Discount = Marked Price – Selling Price

• And Discount Percentage = (Discount/Marked price) x 100

Profit and Loss Formulas

Now let us find profit formula and loss formula.

• The profit or gain is equal to the selling price minus cost price.

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

• Loss is equal to cost price minus selling price.

Profit percentage = (Profit /Cost Price) x 100

Loss percentage = (Loss / Cost price) x 100

The formula for the profit and loss percentage is:

Profit and Loss Examples

• If a shopkeeper brings a cloth for Rs.100 and sells it for Rs.120, then he
has made a profit of Rs.20/-.

• If a salesperson has bought a textile material for Rs.300 and he has to sell
it for Rs.250/-, then he has gone through a loss of Rs.50/-.

• Suppose, Ram brings a football for Rs. 500/- and he sells it to his friend for
Rs. 600/-, then Ram has made a profit of Rs.100 with the gain percentage
of 20%.

These are some common examples of the profit and loss concept in real life,
which we can observe regularly.

Profit and Loss Tricks

As you have learned until now how to calculate profit as well as loss and also the
percentage of them. Now let us learn some tricks or formulas to solve maths
problems based on gain and loss, starting from the general formulas.

1. Profit, P = SP – CP; SP>CP

2. Loss, L = CP – SP; CP>SP
 3. P% = (P/CP) x 100
4. L% = (L/CP) x 100
5. SP = {(100 + P%)/100} x CP
6. SP = {(100 – L%)/100} x CP
7. CP = {100/(100 + P%)} x SP
8. CP = {100/(100 – L%)} x SP
9. Discount = MP – SP
10. SP = MP -Discount
11. For false weight, profit percentage will be P% = (True weight – false
weight/ false weight) x 100.
12. When there are two successful profits say m% and n%, then the net
percentage profit equals to m+n+((mn)/100)
13. When the profit is m% and loss is n%, then the net % profit or loss will be:
(m-n-mn)/100

14. If a product is sold at m% profit and then again sold at n% profit then the
actual cost price of the product will be: CP = [100 x 100 x
P/(100+m)(100+n)]. In case of loss, CP = [100 x 100 x P/(100-m)(100-n)]
15. If P% and L% are equal then, P = L and %loss = P2/100

Quick Tips and Tricks

1) Profit = (S.P.) > (C.P.)

2) Loss = (S.P.) < (C.P.)

3) If profit earned by selling an article is 25 %, then S.P. = 125% of C.P.

4) If an article is sold at a loss of 30 %, then S.P. = 70 % of C.P.

5) A shopkeeper sells two similar items A and B. If A is sold at a gain of x % and

B is sold at a loss of x %, then shopkeeper always incurs a loss given by:

Loss% = Common loss and gain% 2 = x 2

 10 10

6) A trader sells goods at cost price but uses a weight of x kg instead of y

kg (false weights) and makes profit. This profit can be calculated using the
formula shown below:

True weight – False weight = Error

Error
Gain% = × 100 %
(True weight – Error)

7) If cost price of X articles is equal to selling price of Y articles, then profit can
be calculated using the formula:

a) C.P. of X = S.P. of Y
b) Number of X articles > Number of Y articles

No. of X articles – No. of Y articles

Profit% = × 100
No. of Y articles

8) If a seller makes X % above C.P. and offers a discount of Y%, then profit % or
loss % can be calculated using the formula:

X×Y
Profit or Loss% = (X – Y) –
100

9) Discount:

Discount
a) Discount% = × 100
Marked Price (M.P.)

b) If a and b are two successive discount percentages, then single equivalent

discount percentage is given as:

ab
Single equivalent discount percentage = (a + b) –
100
Let us explain the above-given formulas with examples.

Solved Problems

Example. 1: Suppose a shopkeeper has bought 1 kg of apples for 100 rs.

And sold it for Rs. 120 per kg. How much is the profit gained by him?

Cost Price for apples is 100 rs.

Selling Price for apples is 120 rs.

Then profit gained by shopkeeper is ; P = SP – CP

P = 120 – 100 = Rs. 20/-

Example.2: For the above example calculate the percentage of the profit
gained by the shopkeeper.

Answer:

We know, Profit percentage = (Profit /Cost Price) x 100

Therefore, Profit percentage = (20/100) x 100 = 20%.

Example.3: A man buys a fan for Rs. 1000 and sells it at a loss of 15%.
What is the selling price of the fan?

Answer: Cost Price of the fan is Rs.1000

Loss percentage is 15%

As we know, Loss percentage = (Loss/Cost Price) x 100

15 = (Loss/1000) x 100

Therefore, Loss = 150 rs.

As we know, Loss = Cost Price – Selling Price

So, Selling Price = Cost Price – Loss

= 1000 – 150
Selling Price = R.850/-

Example 4: A pen is purchased for Rs. 20 and is sold for Rs. 26. What is the
percentage profit earned?
Answer: Here CP = 20, SP = 26. Profit = SP – CP ⇒ 26 – 20 = Rs. 6.
Profit % = 100 × Profit/Cost Price ⇒ 100 × 6/20 = 30%.

Example 5: A cup is purchased for Rs. 160 and is sold for Rs. 128. What is the
profit or loss percentage?
Answer: Here CP = 160, SP = 128. Profit = SP – CP ⇒ 128 – 160 = -32. Again a
negative profit of 32 means it is a loss.

Example 6 : Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its
repairs. If he sells the scooter for Rs. 5800, his gain percent is:

4
A. 4 %
7

5
B. 5 %
11

C. 10%

D. 12%

Answer:: Option B
Explanation:

Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.

Selling Price (S.P.) = Rs. 5800.

Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.

300 5
Gain % = x 100 =5 %
5500 % 11
Example 7: A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and
another for
Rs. 960 at a loss of 4%. His total gain or loss percent is:

15
A. 5 % loss
17

15
B. 5 % gain
17

2
C. 6 % gain
3

D. None of these

Answer:: Option B
Explanation:
100
C.P. of 1st transistor = Rs. x 840 = Rs. 700.
120
100
C.P. of 2nd transistor = Rs. x 960 = Rs. 1000
96

So, total C.P. = Rs. (700 + 1000) = Rs. 1700.

Total S.P. = Rs. (840 + 960) = Rs. 1800.

100 15
Gain % = x 100 =5 %
1700 % 17

Exercise Problems

Q.1 An article is bought for `600 and sold for `750. What is the profi t
percentage?
 (a) 20%

(b) 25%

(c) 30%

(d) None of these

Q.2 By selling a VCD player for `1950, I got a profi t of 30%. At what price
should I have sold it in order to get a profi t of 40%?

(a) `2000

(b) `2100

(c) `2500

(d) None of these

Q.3 The profi t obtained by selling a book for `56 is the same as the loss obtained
by selling this book for `42. What is the cost price of the book?

(a) `40

(b) `50

(c) `49

(d) None of these

Q.4 A man bought a shirt at 3/4th of its list price and sold it at 50% above its list
price. What is his percentage gain in the transaction?

(a) 50%

(b) 70%

(c) 80%

(d) 100%

Q.5 By selling a CD for `150, a shop owner lost 1/16 of what it costs. What is the
cost price of CD?
 (a) `120

(b) `140

(c) `150

(d) `160

Q.6 Saurabh sold 250 cycles and had a gain equal to the selling price of 50 cycles.
What is his profit percentage?

(a) 25%

(b) 20%

(c) 10%

(d) None of these

Q.7 If profit as a percentage of the selling price is 25%, then what is profit as a
percentage of the cost price?

(a) 25%

(b) 331 3 %

(c) 20%

(d) 15%

Q.8 A man sold an article at a profi t of 10%. If he had charged `45 more his
profit percentage would have been 25%. What is the cost price?

(a) `200

(b) `300

(c) `250

(d) None of these

Q.9 Richa purchased a pen drive at 4/5th of its list price and sold it at 20% above
the original list price. What is Richa’s profit percentage?

(a) 25%
 (b) 40%

(c) 50%

(d) None of these

Q.10 A man buys 200 oranges for `10. How many oranges a rupee can he sell so
that his profit percentage is 25%?

(a) 10

(b) 14

(c) 16

(d) 20

ANSWER KEY

1. B

2. B

3. C

4. D

5. D

6. A

7. B

8. B

9. C

10. C