2. Topics to be covered
Definition & Basic examples
Frequently asked examples
Introduction to Discount and mark up
Combination of Mark up, Discount & profit
Faulty Weight related Examples
Practice examples
3. Profit & Loss Basics
• Common Terms
CP = Cost / Buying price
SP= Selling Price
Profit = SP – CP
Loss = CP – SP
Profit or loss % =
𝑺𝑷−𝑪𝑷 𝑶𝒓 (𝑪𝑷−𝑺𝑷)
𝑪𝑷
* 100 % OR
𝑷𝒓𝒐𝒇𝒊𝒕 𝒐𝒓 𝑳𝒐𝒔𝒔
𝑪𝑷
*100 %
This is exactly same as % change Change in value * 100 %
Initial value
As we already know from the percentage part:
So if we need to increase a value then MF will be (100 + X)/100 %
& if we need to decrease a value then MF will be (100 - X)/100 %
So, equation we need to remember is Initial Value * (M.F) = Final value
Here in profit & loss:
So if there is Profit then MF will be (100 + X)/100 %
& if there is loss then MF will be (100 - X)/100 %
So, equation we need to remember is Cost Price * (M.F) = Selling price
6. Frequently asked Examples
Que: A bought cycle for Rs. 1080. and sold to be at 20% loss. B spent
Rs. 36 on improving the condition and then sold to C at 20% profit.
What amount did C pay for it?
Sol:
For A &B, CP(MF) = SP MF for loss of 20% is 0.8 so
1080 * (0.8) = 864
Now B spent ₹36 more so, total CP = 864 + 36 = 900
Again for B & C, CP(MF) = SP MF for Profit of 20% is 1.2 so
900 * (1.2) = 1080/-, Ans: ₹ 1080/-
7. Frequently asked Examples
Que: A salesman sold one-fourth of his stock at 50% profit, remaining
at 80% profit. What was his total profit % on whole transaction ?
Sol: Suppose He had stock of CP = ₹ 100
SP1+SP2 = 135 + 37.5 = ₹ 172.5, When CP was assumed as ₹ 100
So Profit Percentage is Ans: 72.5%
Short Cut:
50*
𝟏
𝟒
+ 80*
𝟑
𝟒
= 72.5
Only used when Base is common.
1
4
* 100 = 25 = CP1
SP 1= 25 * 1.5
= ₹ 37.5
3
4
* 100 = 75 = CP2
SP 2= 75 * 1.8
= ₹ 135
8. Understanding Relation Between Quantity and CP/SP
Suppose I buy a pen of ₹ 10 and sell it for ₹ 15, what will be my
Profit and profit %?
Very simple Profit is ₹ 5 & percentage =
𝟓
𝟏𝟎
*100 = 50%
Now I buy 7 such pens at ₹10 each and sell all of them at ₹15
each. now what will be my profit and Profit %?
Profit is 105 – 70 = ₹35 and Percentage =
𝟑𝟓
𝟕𝟎
∗ 𝟏𝟎𝟎 = 50%
Observation 1: While changing Quantity, Keeping SP and CP as it is,
the profit % doesn’t change. So, in similar and most of the cases
Profit or Loss% does not depend upon quantity.
Now I buy 7 such pens at ₹10 each and sell only 4 of them at ₹15 each.
now what will be my profit/Loss and Profit/Loss %?
Loss is 70 – 60 = ₹10 and Percentage =
𝟏𝟎
𝟕𝟎
∗ 𝟏𝟎𝟎 = 14.28% loss is this correct?
NO !!! Its not correct. Why?? What about other 3 pens then?? We cant say
anything about Profit and loss until we don’t know about those pens.
Observation 2: To find Profit or Loss % we need SP and CP of equal
quantity, in this and most of the cases.
9. Frequently asked Examples
Que: Amit bought equal quantities of two types of oranges, one at the rate of
₹ 200 for 4 Kgs and other at the rate of ₹ 400 for 10 Kgs. He mixed both and
sold at the rate ₹ 50 per Kg. What is his profit or Loss percentage?
Options: A. 16.66 % Profit B. 14.28% Profit C. 11.11% Profit D. 10% Loss
Sol: As we already know, we need equal quantity of buying and selling for
profit or loss % so, here we try to find Price of 1 Kg.
For CP,
CP𝟏 ₹200/4Kgs ₹50/Kg
CP𝟐 ₹400/10 Kgs ₹40/Kg
SP ₹ 50/Kg, so now we have CP and SP of 1KG(same quantity) hence,
Profit/Loss % =
𝟓
𝟒𝟓
*100 = Ans : 11.11% Profit
Common Mistakes:
Students take 14 Kg in total but its clearly mentioned in first line of question
that he bought equal quantities. The given are rates and not exact quantity.
He mixed both
So ₹ 90 / 2 Kg or
₹ 45/Kg
10. Frequently asked Examples
Que: Aditya purchases toffees @ ₹ 10 per dozen and sells @ ₹ 12 for 10
toffees. Find his profit percentage.
Options: A. 30% B. 44% C. 18% D. 25%
Sol: here also we can Find the price of 1 toffee and solve as we did in last
question. But to avoid fractions we can go for another common quantity as
we already know that quantity doesn’t change P or L percentage.
So For same quantity i.e. 120 we have SP = 144 and CP = 100, Clearly
Ans = 44% Profit
Quantity Price
CP 12 10
SP 10 12
* 10 = 120 * 10 = ₹ 100
* 12 = 120 * 12 = ₹ 144
11. Frequently asked Examples
Que: A reduction of 10% in the price of sugar enables a man to buy 25Kg
more sugar for ₹ 225. What was original price of Sugar?
Options: A. ₹ 1/kg B. ₹ 25/kg C. ₹ 0.9/kg D.Can’t be Determined
Sol:
Let be original Price of sugar = ₹ X/kg
Then Reduced price = 0.9X/kg
As given,
𝟐𝟐𝟓
𝟎.𝟗𝒙
-
𝟐𝟐𝟓
𝒙
= 25, Solving for X,
Ans: X = ₹ 1/Kg
Method 2: Exp = Price * consumption
So reduction of 10% in price would enable a person to buy 11.11%
more quantity, keeping Expenditure constant.
So if we assume original quantity as X then,
So 11.11%
𝟏
𝟗
* X = 25 Kg, X = 225 kg which did cost ₹225
So original price =
𝟐𝟐𝟓
𝟐𝟐𝟓
= ₹ 1/Kg
12. Frequently asked Examples
Que: Krish has 12 eggs, he sells x eggs at profit of 10% and remaining eggs at
loss of 10%, on overall transaction he gained 5%. Then find X.
Options: A. 7 B. 9 C. 5 D.6
Sol: let the CP of each egg be ₹ 1 then, then as given
CP1 * MF1 + CP2 * MF2 = Total CP * Overall MF
₹ X (1.1) + ₹(12-X) (0.9) = ₹12 * (1.05) , solving
Ans: X = 9 eggs
Remarks: Check options as well
13. Frequently asked Examples
Que: Alia sells 40 pencils and gains the amount equal to SP of 10 pencils, find
the Profit %.
Options: A. 20% B. 25% C. 33.33% D. 40%
Sol:
SP of 40 – CP of 40 = SP of 10
SP of 30 = CP of 40 = Assume ₹ 120 (Can be assumed anything)
SP of 1 pencil = ₹ 4 , CP of 1 pencil = ₹ 3,
Profit % =
𝟏
𝟑
*100
Ans: 33.33%
Short cut: IF we get SP of X quantity = CP of Y quantity, then we can take
SP = ₹ Y & CP = ₹ X and find profit or loss %
So in above example SP of 30 = CP of 40
We can take CP = ₹ 30 and SP = ₹ 40
Profit% =
𝟏𝟎
𝟑𝟎
* 100 = 33.33%
14. Frequently asked Examples
Similar Que: By selling 33 meters of clothes Shraddha loses amount equal to
cost price of 11 meters. Find loss %.
Options: A. 20% B. 25% C. 33.33% D. 40%
Sol:
CP of 33 – SP of 33 = CP of 11
SP of 33 = CP of 22 = Assume ₹ 66 (Can be assumed anything)
SP of 1 pencil = ₹ 2 , CP of 1 pencil = ₹ 3,
Loss % =
𝟏
𝟑
*100
Ans: 33.33%
Short cut: IF we get SP of X quantity = CP of Y quantity, then we can take
SP = ₹ Y & CP = ₹ X and find profit or loss %
So in above example SP of 33 = CP of 22
We can take CP = ₹ 33 and SP = ₹ 22
Loss% =
𝟏𝟏
𝟑𝟑
* 100 = 33.33%
15. Frequently asked Examples
Que A: Cost Price of Two articles are same, ₹ 9900/-. One is sold at 10% Profit
and other is sold at 10% loss. Find overall Profit or loss %.
Que B: Selling Price of Two articles are same, ₹ 9900/-. One is sold at 10%
Profit and other is sold at 10% loss. Find overall Profit or loss %.
Sol:
Que A: SP𝟏 = 9900*1.1 = ₹ 10890 & SP𝟐 = 9900*0.9 = ₹ 8910
Total SP = 10890 + 8910 = ₹ 19800, Total CP given = 9900*2 = ₹ 19800
Ans: No Profit No loss
Que B: CP𝟏 = 9900/1.1 = ₹ 9000, CP𝟐 = 9900/0.9 = ₹ 11000,
Total CP = 9000 + 11000 = 20000, Total SP given = 9900*2 = ₹ 19800
Loss % =
𝟐𝟎𝟎
𝟐𝟎𝟎𝟎𝟎
*100 = 1% loss
Short Cut: When Selling Price of Two articles are same, (Anything). One is sold
at x % Profit and other is sold at x% loss then overall it will always be loss of
X²
𝟏𝟎𝟎
%
In our case
𝟏𝟎2
𝟏𝟎𝟎
= 1% loss
16. Introduction to Discount & Mark-up
MP Marked Price – The price which is marked on the Item
Disc % =
𝑴𝑷 −𝑺𝑷
𝑴𝑷
* 100% & MP (MF) = SP
0.__ Discount (similar to decrease)
1.__ Tax, if any (similar to Increase)
E.g. 1: A jeans is marked ₹ 3000 but You buy it in ₹ 1200 only. Find Disc%
Disc % =
𝑴𝑷 −𝑺𝑷
𝑴𝑷
* 100 =
𝟑𝟎𝟎𝟎−𝟏𝟐𝟎𝟎
𝟑𝟎𝟎𝟎
* 100 = 60 %
E.g. 2: A T-shirt marked ₹ 1500, & store has mentioned 30% disc. Find SP.
MP (MF) = SP 1500 (0.7) = SP ₹ 1050
Marked Price Selling Price % Disc or % Tax
700 550 ? % Disc
1700 1785 ? % Tax
2100 ?? 35% Disc
?? 2790 38% Disc
?? 1230 2.5% Tax
5000 ?? 25% disc & 10% Tax
17. Introduction to Discount & Mark-up
In Last Example: If we apply Tax first and then Disc, will it make a difference?
No, as we can see it will be either 5000 * 0.75 * 1.1 or 5000 * 1.1 * 0.75
Both will be same.
Marked
Price
Selling Price % Disc or % Tax MF Answer
700 550 ? % Disc -- 21.42% Disc
1700 1785 ? % Tax -- 5% Tax
2100 ?? 35% Disc 2100*0.65 1365
?? 2790 38% Disc 4500
?? 1230 2.5% Tax 1200
5000 ?? 25% disc & 10%
Tax
5000 * 0.75 * 1.1 4125
18. Combination of Mark up, Discount & Profit
CP SP MP
E.G:
Profit %
1.__
Loss %
0.__
Tax %
1.__
Disc %
0.__
Mark up %
1.__
CP SP MP
Que: A shopkeeper allows disc. of 20% after marking all articles 40% above
cost price. Find his profit %.
Profit %
20% ??
Disc
20%
40% above
Mark up
Wrong
19. Frequently asked Examples
Que: A shopkeeper allows disc. of 20% after marking all articles 40% above
the cost price. Find his profit %.
Options: A. 20% B. 15% C. 12% D. None
Sol:
Method 1: Assume CP as ₹ 100, then marked price will be ₹ 100 * 1.4 = ₹ 140.
Now Disc is given on MP, MP(MF) = SP 140(0.8) = ₹112.
Assumed CP = ₹ 100, SP = ₹112 So clear profit is 12%
Method 2: Same as Successive % change Equation
Profit or Loss Percentage = Markup % - Disc% -
𝑴𝒂𝒓𝒌 𝒖𝒑∗𝑫𝒊𝒔𝒄
𝟏𝟎𝟎
= +40 – 20 –
𝟒𝟎∗𝟐𝟎
𝟏𝟎𝟎
= 12%
Method 3:
MF 𝒐𝒇 𝑷𝒐𝒓 𝑳 = MF 𝒐𝒇 𝑴𝒂𝒓𝒌𝒖𝒑 * MF 𝒐𝒇 𝑫𝒊𝒔𝒄
= 1.4 * 0.8 = 1.12
MF of profit or loss as 1.12 indicates 12% profit
20. Frequently asked Examples
Que: A dealer allows disc of 7% on cash payments, how much % above the
cost price should he mark to make profit of 10%?
Sol:
Method 1: Assume CP as ₹ 100, then Seling price will be ₹ 100 * 1.1 = ₹ 110.
Now Disc is given on MP, MP(MF) = SP X (0.93) = ₹110 X =
𝟏𝟏𝟎
𝟎.𝟗𝟑
= 118.27
Assumed CP = ₹ 100, MP = ₹118.27 So clear Mark up % is 18.27%
Method 2:
Profit or Loss Percentage = Markup % - Disc% -
𝑴𝒂𝒓𝒌 𝒖𝒑∗𝑫𝒊𝒔𝒄
𝟏𝟎𝟎
10 = +X – 7 –
𝐱 ∗𝟕
𝟏𝟎𝟎
X = 18.27%
Method 3:
MF 𝒐𝒇 𝑷𝒐𝒓 𝑳 = MF 𝒐𝒇 𝑴𝒂𝒓𝒌𝒖𝒑 * MF 𝒐𝒇 𝑫𝒊𝒔𝒄
1.1 = X * 0.93 X = 1.1827
MF of markup as 1.1827 indicates 18.27%.
21. Frequently asked Examples
Que: 2 T-shirts free with every 3 T-shirts. Find Disc %.
Sol:
Assume MP of each item as ₹100
Then you are taking items of ₹ 500 but paying only for 3 items which is ₹ 300
So Disc % =
𝑴𝑷 – 𝑺𝑷
𝑴𝑷
* 100
𝟓𝟎𝟎 – 𝟑𝟎𝟎
𝟓𝟎𝟎
* 100 = Ans : 40%
22. Frequently asked Examples
Que: Shop A offers flat disc of 60%, where as Shop B offers successive Disc of
30% and again 30%, and Shop C offers three successive disc of 20% each on
the same item marked same at all shops at ₹5000. Find selling prices of all
shops and net discount at Shop B and Shop C.
Sol: As we know MP (MF) = SP
Shop A 5000 * 0.4 = ₹ 2000
Shop B 5000 * 0.7*0.7 = 5000 * 0.49 = ₹ 2450
Shop C 5000 * 0.8 * 0.8 * 0.8 = 5000 * 0.512 = ₹ 2560
Net Disc at Different shops
Shop A 60% given
Shop B 51%
Shop C 48.8%
23. Faulty weights examples
Que: A dishonest dealer claims to sell Rice at cost price but uses a false
weight of 960 Grams instead of 1 kg. Find his Profit %.
Option: A. 40% B. 10% C. 4% D. 4
𝟏
𝟔
%
Sol: Assume CP of 1 gram of rice = ₹ 1.
So CP of 960 gm = ₹ 960
& CP of 1 kg = ₹ 1000
Now he is selling only 960gm at cost price so his expense is ₹ 960
But on the other hand customer thinks he is getting 1Kg so he pays CP of 1 kG
which is ₹ 1000.
So ultimately for dealer CP = ₹ 960, SP = ₹ 1000
Profit % =
𝟒𝟎
𝟗𝟔𝟎
* 100 = 4
𝟏
𝟔
%
24. Faulty weights examples
Que: A weighing balance shows 900 gm for 1 Kg due to error at a dealer’s
shop but dealer has marked up all goods by 20%. Find his Profit %.
Sol: Assume CP of 1 gram of goods = ₹ 1.
SO CP of 1 Kg = ₹ 1000
& CP of 900 gm = ₹ 900
so MP of 900 gm = 900 * 1.2 = ₹ 1080.
Now he is selling 1 kg so his expense is ₹ 1000
But on the other hand customer thinks he is getting 900 gms(due to scale
error) so he pays MP of 900 gms which is ₹ 1080
So ultimately for dealer CP = ₹ 1000, SP = ₹ 1080
Profit % =
𝟖𝟎
𝟏𝟎𝟎𝟎
* 100 = 8 %
Short Cut:
-10 + 20 –
𝟏𝟎∗𝟐𝟎
𝟏𝟎𝟎
= 8%
25. Faulty weights examples
Que: In winters the meter scale shrinks by 10% of its actual length, but
knowing this, in it’s regular condition the meter scale was already rigged to
measure 10% more than it is supposed, what % of profit or loss the cloth
merchant makes in winter?
Options: A. 1 % profit B. 1.0101% loss C. 1% Loss D. 1.0101% Profit
Sol:
A normal meter scale measures 100 cm
Now its rigged to measure 10% more 110 cm
Now in winter the rigged scale shrinks by 10% then 110*0.9 = 99 cm
So, now in winter when dealer measures with the same scale, it will measure
99 cm, but on the customer end, he feels it’s a Meter scale so he will pay for
100 cm
So ultimately for Dealer we can think like CP = ₹ 99 , SP = ₹ 100
Profit % =
𝟏
𝟗𝟗
* 100 = 1.0101%
26. Practice Examples
Que: A man sells articles at profit of 25%. If he had bought it at 20% less &
sold for ₹ 10.50 less, then he would have gained 30%. Find original CP of
article.
Sol: Assume
CP1 = X , now as we know SP = CP(MF) SP1 = 1.25*X
Bought at 20% less CP2 = 0.8 * X & sold for ₹10.50 less SP2 = 1.25*X -10.50
Then he would have gained 30%. That means according to new CP & SP the
profit % will be 30%.
CP𝟐 * (MF) = SP𝟐
0.8* X * (1.3) = (1.25*X – 10.50) solving this we get
Ans: X = ₹50
27. Practice Examples
Que: Mr. Sharma offers successive disc of 5% and 15%, where as Mr.Verma
offers successive Disc of 8% & 12%. Final selling price in both case was same,
then find Ratio of their marked prices.
A. 0.9974 B. 1.0482 C. 1.0092 D. 1.0026
Sol: As we know Marked Price (MF) = Selling Price
MPsharma (MF1s) (MF𝟐𝑺) = SPsharma
MPverma (MF𝟏𝒗) (MF𝟐𝒗) = Spverma
Then now as given both SP are same so,
MPsharma (MF𝟏𝒔) (MF𝟐𝒔) = MPverma (MF𝟏𝒗) (MF𝟐𝒗)
M𝑷sharma / MPverma = (MF𝟏𝒗) * (MF𝟐𝒗) = 0.92 * 0.88 = 1.0026
(MF𝟏𝒔) (MF𝟐𝒔) 0.95 * 0.85
28. Practice Examples
Que: Given CP of 10 oranges = CP of 1Kg of Apples
CP of 12 Apples = CP of 1 Kg of oranges
SP of 15 Oranges = SP of 1 Kg Apples
SP of 1 Kg Oranges = SP of _??_ Apples
Sol: Lets Assume CP of 1 Orange = Oc, CP of 1 Apple = Ac
also assume 1 kg of Apple contains X apples
& 1 kg of Oranges contains Y Oranges
Now as given 10 * Oc = X * Ac ----- Eq. 1
Y * Oc = 12 * Ac ----- Eq. 2
Now Lets assume SP of 1 Orange = OS, SP of 1 Apple = AS
Now as given 15 * OS = X * AS ------ Eq. 3
Y * OS = _ * AS ------ Eq. 4
Solving, P =
𝒀 ∗ 𝑶𝒔
𝑨𝒔
=
𝒀 ∗𝑿
𝟏𝟓
(As
𝑶𝒔
𝑨𝑺
=
𝑿
𝟏𝟓
from Eq. 3)
So we need to find P =
𝑿 ∗ 𝒀
𝟏𝟓
, now to find value of X * Y use Eq.1 & 2
Divide Eq. 1 by Eq. 2 10 * Oc = X * Ac X * Y = 120
Y * Oc = 12 * Ac
So P =
𝟏𝟐𝟎
𝟏𝟓
= Ans: 8
P
29. Practice Examples
Que: A machine produces articles @ 50 units/hour. The articles are sold for
₹ 100 each & cost of production is ₹ 40 Each. However 20% of articles are
defective and can’t be sold. Now, the production rate can be increased but
every increase of X units/Hour would increase the production cost by 2X% &
number of defectives would become (20+1.5X)%. What is maximum increase
in production that can be undertaken without incurring losses?
Options: A. 14 B. 18 C. 17 D. 16
Sol: Lets assume we increase production by X units, then
CP after Increase (50+X) * 40 * [
𝟏𝟎𝟎+𝟐𝑿
𝟏𝟎𝟎
]
SP after Increase (50+X) * 100 * [
𝟏𝟎𝟎 −(𝟐𝟎+𝟏.𝟓𝑿)
𝟏𝟎𝟎
]
Now for profit SP > CP,
Solving we get a quadratic Equation 2.3X² + 75X – 2000 < 0
Now we can go from options, as we need highest we can start from
Highest i.e 18
Putting X = 18 in equation we get 95.2 < 0, so does not satisfy.
Putting X = 17 in equation we get -60.3 < 0, So satisfies.
Hence Ans = 17
30. Doubts?
• Do you particularly require revision of any topic ?
• Did you not understand any particular example?
• Or any thing else?
• Feel free to ask.
