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Preface
The Digi-notes (Profit/Loss/Discount) as presented here is prepared strictly
according to IBPS-PO, IBPS-Clerk, IBPS-SO and other PO/Clerk level competitive
exams. The main aim of the Digi-notes is to develop the notion of the Profit, Loss
and Discount so that candidate would be able to handle the quantitative
problems of the real world easily and conveniently and hence in their competitive
exams. Candidates are advised to handle the Digi-notes by pre-assuming that
they are going to learn that how to apply the concept of Profit, Loss and Discount
in quantitative problems and hence to equip ourselves to minimize the steps
required to conclude the answer and finally to develop the SHORT TRICKS.
All the best…
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Contents
1. Preface …………………………………………………………..………………… 2
2. Contents …………………………………………………………………………… 3
3. Introduction ……………………………………………………………………… 4
4. Concept of Cost Price, Selling Price and Marked Price ...………4
5. Strategy..……………………………………………………………………………. 8
6. Questions Based on Application of Unitary Method ………......9
7. How to Calculate the Percentage Profit/ Percentage Loss ....15
8. The Relation Between Cost Price, Marked Up Price
And Selling Price ...……………………………………………………….…….21
9. Miscellaneous Questions ………………………….………………..….….26
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Introduction:
Knowingly or unknowingly; in day to day life; we are using either profit or loss or
discount term while buying or selling an articles. But At large scale; in business
applications; as everything is RELATIVE in this world; the terms Percentage Profit
or Percentage Loss or Percentage Discount is extensively used. Hence what is our
main focus is to relate the Absolute things (The Profit or loss or Discount) to its
relative counterpart (The Percentage Profit or Percentage loss or Percentage
Discount). It is clear that the Percentage is going to play a lead role in the entire
game of Profit/Loss/Discount.
We would not learn a single formula for answering the questions of
Profit/Loss/Discount. We will just relate each and every concept of
Profit/Loss/Discount to the Percentage and hence apply the tools of percentage
language as discussed in our previous Digi-Notes for answering the questions and
hence to create the Short Tricks.
The Concept of Marked Price, Cost Price, and Selling Price?
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The printed/listed/tagged price of an article is called its marked price.
Keep in mind that Cost price and the Selling price are relative terms. We cannot
define it absolutely; we have to specify about which person or article we are
dealing with. The SAME PRICE would act as cost price according to one context
while as selling price according to another. To differentiate it:
The money which comes out of the pocket of a person; is called the cost
price for that person.
The money which goes into the pocket of a person; is called the selling price
for that person.
Now from the discussion below; we will correlate the concept of
profit/loss/discount to the percentage:
1. Suppose a man built a chair which costs him a total of Rs.1500 (Raw
Material + Manufacturing + Transportation + Labour Charge etc.).
i. If he sold it for Rs.1750; then what would you say; he incurs profit or
Loss? Of course profit; why…! Because He sold it at a price higher
than what it actually costs him? Hence:

If SP > CP; it implies the Profit incurs. Hence difference
of SP and CP would be quantitatively taken as the amount of
profit.
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𝑷𝒓𝒐𝒇𝒊𝒕 = 𝑺𝒆𝒆𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆 − 𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆
(2) Now if he sold it for Rs.1400; then this time what would you say
whether he incurs profit or Loss? Of course loss; why…!
Because He sold it at a price lower than what it actually costs him?
Hence:

If SP < CP; it implies the Loss incurs. Hence difference
of CP and SP would be quantitatively taken as the amount of
loss.
𝑳𝒐𝒔𝒔 = 𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆 − 𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆
𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆
𝐒𝐏 > CP
𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆
𝐒𝐏 < CP
𝐏𝐫𝐨𝐟𝐢𝐭
𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆
𝐋𝐨𝐬𝐬
(ii) What we perceive from the above discussion that; there might always be
either increase (In case of Profit) or decrease (In case of loss) from the same
base value; the CP. OK….!!! We concluded an important point…… Here CP acts
as the BASE VALUE; and we already know that the base value is always taken
as 100%.
CP is always 100% (In case when incurs either profit or loss)
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𝑷𝒓𝒐𝒇𝒊𝒕
𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆 = 100%
(𝑩𝒂𝒔𝒆 𝒗𝒂𝒍𝒖𝒆)
𝑳𝒐𝒔𝒔
2. Now we could easily digest the following two points for handling the
question
i.
In case of Profit:
𝐒𝐏 = 110%
% P = 10%
ii.
𝐂𝐏 = 100%
In case of Loss:
% L = 20%
𝐂𝐏 = 100%
𝐒𝐏 = 80%
Page 7 of 33
3. Keep in mind that; discount is always given by the shopkeeper. Also unless
and otherwise mentioned in the question; discount is always given on the
Marked price (never on cost price), which is the initial/base value in case
of discount. So this time we concluded that MP is always 100%. Clearly after
offering the discount (i.e. after decreasing the price); the shopkeeper
would SOLD it to the customer.
𝐌𝐏 = 100%
% D = 30%
(Base value)
𝐌𝐏 = 100%
Discount
𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆
𝐒𝐏 = 70%
Strategy:
In forthcoming discussion what we are going to do…..we are just going to simply
PRACTICE some more questions on Percentage. We would handle the questions
of the Profit/Loss/Discount according to the following strategy (Our main aim
would be to develop the logical steps which would make us psychologically strong
enough to evolve the so called SHORT TRICKS of a question):
1. Questions Based on the Application of Unitary Method of Percentage.
2. How to Calculate the Percentage Profit/ Percentage Loss
3. The Relation Between Cost Price, Marked Up Price and Selling Price
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4. Miscellaneous Questions
Questions Based on the Application of Unitary Method of Percentage:
In this section we will discuss only those questions which could be easily solved
with the help of the application of unitary method. Recall from the Digi-notes of
the percentage to approach the question:
𝑽𝒂𝒍𝒖𝒆
𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆 𝒗𝒂𝒍𝒖𝒆
× 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆 𝑽𝒂𝒍𝒖𝒆 𝒘𝒉𝒊𝒄𝒉 𝒊𝒔 𝑨𝒔𝒌𝒆𝒅
Q.1: A man bought an article for Rs.425. For how much should he sell it
in order to gain 8%?
Short Trick:
Sol:
𝑹𝒔.𝟒𝟐𝟓
= 𝟏𝟎𝟎% × 𝟏𝟎𝟖%
= 𝑹𝒔. 𝟒𝟓𝟗
Q.2: A shopkeeper bought the books from a wholesaler for Rs.6250.
Find at what price should he sell it in order to lose 10%?
Page 9 of 33
Short Trick:
Sol:
=
𝑹𝒔.𝟔𝟐𝟓𝟎
𝟏𝟎𝟎%
× 𝟗𝟎%
= 𝑹𝒔. 𝟓𝟔𝟐𝟓
Q.3: A fruit seller sold the fruits for Rs.3900 and gains 20%. Find at what
price did he bought the fruits?
Short Trick:
Sol: =
𝑹𝒔.𝟑𝟗𝟎𝟎
𝟏𝟐𝟎%
× 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟑𝟐𝟓𝟎
Q.4: I sold a book for Rs.705.76, and loosed 12%. Find the cost price of
the book.
Short Trick:
𝑹𝒔.𝟕𝟎𝟓.𝟕𝟔
Sol: =
× 𝟏𝟎𝟎%
𝟖𝟖%
= 𝑹𝒔. 𝟖𝟎𝟐
Q.5: A man sold an article for Rs.250 and thereby gain 25%. Find how
much amount did he gains?
Short Trick:
𝑹𝒔.𝟐𝟓𝟎
Sol: = 𝟏𝟐𝟓% × 𝟐𝟓%
= 𝑹𝒔. 𝟓𝟎
Page 10 of 33
Q.6: A man build a chair and sold it at a profit 7.5% and thereby gains
Rs.375. Find the total amount which costs him to build the chair?
Short Trick:
𝑹𝒔.𝟑𝟕𝟓
Sol: = 𝟕.𝟓% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟓𝟎𝟎𝟎
Q.7: A trader sold the rice at a loss of 2% and thereby bears a loss of
Rs.120. Find at what price did he sold the rice?
Short Trick:
𝑹𝒔.𝟏𝟐𝟎
Sol: = 𝟐% × 𝟖𝟖%
= 𝑹𝒔. 𝟓𝟐𝟖𝟎
Q.8: A trader sold a horse for Rs.5700 and thereby loses 5%. Find at
what price should he sold the horse in order to gain 5%?
Short Trick:
𝑹𝒔.𝟓𝟕𝟎𝟎
Sol: = 𝟗𝟓% × 𝟏𝟎𝟓%
= 𝑹𝒔. 𝟔𝟑𝟎𝟎
Q.9: By selling an article for Rs.195 a dealer makes a profit of 30%. By
how much should he increase his selling price so as to make a profit of
40%?
Short Trick:
𝑹𝒔.𝟏𝟗𝟓
Sol: = 𝟏𝟑𝟎% × (𝟏𝟒𝟎% − 𝟏𝟑𝟎%)
= 𝑹𝒔. 𝟏𝟓
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Q.10: I sold a book at a profit of 27%. If I sold it for Rs.36 more; 33%
would have been gained. Find the cost price of the book?
Short Trick:
𝑹𝒔.𝟑𝟔
Sol: = 𝟑𝟑%−𝟐𝟕% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟔𝟎𝟎
Q.11: A trader sold a radio at a loss of 7%. If he sold it for Rs.16 more;
his loss reduces to 5%. Find at what price did he bought the radio?
Short Trick:
𝑹𝒔.𝟏𝟔
Sol: = (−𝟓)%−(−𝟕)% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟖𝟎𝟎
Question 12: A trader sold a horse at a loss of 6%. If he sold it for Rs.640 more; he
would have been gained 10%. Find the cost price of the horse?
Short Trick:
𝑹𝒔.𝟔𝟒𝟎
Sol: = 𝟏𝟎%−(−𝟔)% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟒𝟎𝟎𝟎
Q.13: A man sold a radio at a loss of 2.5%. If he sold it for Rs.100 more;
he gains 7.5%. Find at what price should he sell it in order to gain
12.5%?
Short Trick:
𝑹𝒔.𝟏𝟎𝟎
Sol: = 𝟕.𝟓%−(−𝟐.𝟓)% × 𝟏𝟏𝟐. 𝟓%
= Rs.1125
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Q.14: A man tagged a refrigerator at 15% discount for sell. If he offered
a discount of Rs.1050 to a customer; find at what price did he sold it to
the customer?
Short Trick:
𝑹𝒔.𝟏𝟎𝟓𝟎
Sol: = 𝟏𝟓% × 𝟖𝟓%
= 𝑹𝒔. 𝟓𝟗𝟓𝟎
Q.15: A shopkeeper sold a TV at a discount of 24% on marked price. If
the customer paid Rs.6536 for the TV; find the marked price of the TV.
Short Trick:
𝑹𝒔.𝟔𝟓𝟑𝟔
Sol: = 𝟕𝟔% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟖𝟔𝟎𝟎
Q.16: Amit bought an LCD TV at a discount of 20%. Later he calculated
that if he bought it at 25% discount; he would be able to get Rs.500
more discount. Find at what price did he bought the LCD TV?
Short Trick:
𝑹𝒔.𝟓𝟎𝟎
Sol: = 𝟐𝟓%−𝟐𝟎% × 𝟖𝟎%
= 𝑹𝒔. 𝟖𝟎𝟎𝟎
Page 13 of 33
Q.17: Find the single discount of three successive discount of 10%, 20%
and 30%?
Short Trick:
Sol:
𝐍𝐞𝐭 𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭
= 𝐍𝐞𝐭 𝐄𝐟𝐟𝐞𝐜𝐭(𝟏𝟎%− , 𝟐𝟎%− , 𝟑𝟎%− )
= −𝟒𝟗. 𝟔%
Q.18: The marked price of an article is Rs.16000. After two successive
discounts it is sold for Rs.11400. If the first discount is 5%, then find the
rate of second discount?
Short Trick:
Sol:
𝟓%−
Rs.16000
𝑿=
𝟏𝟔𝟎𝟎𝟎
𝟏𝟎𝟎%
× 𝟗𝟓%
= 𝑹𝒔. 𝟏𝟓𝟐𝟎𝟎
𝑿%
-
Rs.11400
𝟏𝟏𝟒𝟎𝟎 − 𝟏𝟓𝟐𝟎𝟎
× 𝟏𝟎𝟎 = −𝟐𝟓 = 𝟐𝟓% 𝑫𝒊𝒔𝒄𝒐𝒖𝒏𝒕
𝟏𝟓𝟐𝟎𝟎
Q.19: What is the difference between a 45% discount on Rs.1000 and
successive discounts of 30% and 10% on the same amount?
Short Trick:
Sol:
𝐍𝐞𝐭 𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭
= −𝟑𝟎 − 𝟏𝟎 +
𝟑𝟎 × 𝟏𝟎
= −𝟑𝟕%
𝟏𝟎𝟎
𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐃𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐑𝐬. 𝟏𝟎𝟎𝟎
=
× (𝟒𝟓 − 𝟑𝟕)%
𝟏𝟎𝟎%
= 𝐑𝐬. 𝟖𝟎
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How to Calculate the Percentage Profit/ Percentage Loss/Percentage Discount:
This section uses the ability of how accurately you are able to calculate
the percentage value (Which we have already discussed in our previous
Digi Notes-Percentage).
Recall that; while calculating the percentage profit/loss; try to extract
the “cost price; whether it is the exact valued or the relative valued”
(from which profit or loss is compared); then then put it in the
denominator and then multiply the quantity so obtained by 100 and
finally put “%” sign after that (just to nullify the multiplication by 100,
𝟏
its equivalent “% ≡ 𝟏𝟎𝟎” should be multiplied).
Unless or otherwise mentioned in the question; we would put CP
always in the denominator. If it is specified in the question that the
profit/loss is to be calculated on SP; then in that case we would put SP
in the denominator.
Q.1: Alfred buys an old scooter for Rs.4700 and spends Rs.800 for its
repair. If he sells the scooter for Rs.5800, find his gain percentage.
Short Trick:
Sol: %𝐏 =
𝐑𝐬.𝟓𝟖𝟎𝟎−(𝐑𝐬.𝟒𝟕𝟎𝟎+𝐑𝐬.𝟖𝟎𝟎)
×
𝐑𝐬.𝟒𝟕𝟎𝟎+𝐑𝐬.𝟖𝟎𝟎
𝟏𝟎𝟎
𝟓
= 𝟓 𝟏𝟏 %
Page 15 of 33
Q.2: A dishonest shopkeeper professes to sell his goods at cost price,
but he uses a weight of 900gm instead of a kg. Find
1) The profit percentage of the shopkeeper.
2) The loss percentage of the customer.
Short Trick:
𝟏𝟎𝟎 𝐠𝐦
Sol.1: %𝐏 = 𝟗𝟎𝟎 𝐠𝐦 × 𝟏𝟎𝟎
𝟏
= 𝟏𝟏 𝟗 %
Short Trick:
𝟏𝟎𝟎 𝐠𝐦
Sol.2: %𝐏 = 𝟏𝟎𝟎𝟎 𝐠𝐦 × 𝟏𝟎𝟎
= 𝟏𝟎%
𝒕𝒉
Q.3: The cost price of an article is 𝟓⁄𝟕 of the selling price. Find the
percentage profit or the percentage loss.
Short Trick:
Sol: 𝐂𝐏 ∶ 𝐒𝐏 = 𝟓: 𝟕
𝟐
∴ %𝐏 = (𝟓 × 𝟏𝟎𝟎) %
= 𝟒𝟎%
Page 16 of 33
𝟒
Q.4: The profit earned by selling an article is 𝟐𝟖 𝟕 % of the selling price.
Find the percentage profit.
Short Trick:
𝟒
𝟐
Sol: 𝟐𝟖 𝟕 % ≡ 𝟕
𝐏: 𝐒𝐏 = 𝟐: 𝟕
𝟐
%𝐏 = (𝟓 × 𝟏𝟎𝟎) % = 𝟒𝟎%
Q.5: 20% profit on selling price is what percent profit on cost price?
Short Trick:
Sol:
𝐏 ∶ 𝐒𝐏 = 𝟐𝟎 ∶ 𝟏𝟎𝟎
= 𝟏∶ 𝟓
𝟏
%𝐏 = (𝟒 × 𝟏𝟎𝟎) % = 𝟐𝟓%
Q.6: 10% loss on cost price is what percent loss on selling price?
Short Trick:
Sol:
𝐋 ∶ 𝐂𝐏 = 𝟏𝟎 ∶ 𝟏𝟎𝟎
= 𝟏 ∶ 𝟏𝟎
𝟏
𝟏
%𝐋 = (𝟗 × 𝟏𝟎𝟎) % = 𝟏𝟏 𝟗 %
Q.7: If the selling price is tripled; the profit becomes four times; find
the percentage profit on the actual selling price?
Page 17 of 33
Sol: Cost price never changes on changing the selling price. As when
selling price changes; profit/loss accordingly changes to nullify the
change.
If S be the original selling price and P be
the original profit.
𝐒−𝐏= 𝟑×𝐒−𝟒×𝐏
→ 𝟐 × 𝐒𝐏 = 𝟑 × 𝐏
→ 𝐒𝐏: 𝐏 = 𝟑: 𝟐
𝟐
∴ %𝐏 = × 𝟏𝟎𝟎 = 𝟐𝟎𝟎%
𝟏
Q.8: A man sold 9 articles equal to the cost price of 10 articles. Find the
percentage profit or percentage loss incurred.
Sol: Let C and S be the cost price and the selling price of one article;
respectively.
𝟏𝟎 × 𝐂 = 𝟗 × 𝐒
→ 𝐂𝐏: 𝐒𝐏 = 𝟗: 𝟏𝟎
𝟏
∴ %𝐏 = ( × 𝟏𝟎𝟎) %
𝟗
𝟏
= 𝟏𝟏 %
𝟗
Q.9: A fruit seller sold 33 mangoes and gains the selling price of 11
mangoes. Find the percentage profit of the fruit seller.
Sol: Let C and S be the cost price and the selling price of one mango;
respectively.
𝐒𝐏 − 𝐂𝐏 = 𝐏
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→ 𝟑𝟑 × 𝐒 − 𝟑𝟑 × 𝐂 = 𝟏𝟏 × 𝐒
→ 𝟐𝟐 × 𝐒 = 𝟑𝟑 × 𝐂
→ 𝐒: 𝐂 = 𝟑𝟑: 𝟐𝟐 = 𝟑: 𝟐
𝟏
∴ %𝐏 = (𝟐 × 𝟏𝟎𝟎) % = 𝟓𝟎%
Short Trick:
Sol:
𝐏 ∶ 𝐂𝐏 = 𝟏𝟏 ∶ (𝟑𝟑 − 𝟏𝟏)
= 𝟏𝟏 ∶ 𝟐𝟐
= 1:2
𝟏
%𝐏 = (𝟐 × 𝟏𝟎𝟎) % = 𝟓𝟎%
Q.10: A fruit seller sold 66 mangoes and gains the cost price of 22
mangoes. Find the percentage profit of the fruit seller.
Sol: Let C and S be the cost price and the selling price of one mango;
respectively.
𝐒𝐏 − 𝐂𝐏 = 𝐏
→ 𝟔𝟔 × 𝐒 − 𝟔𝟔 × 𝐂 = 𝟐𝟐 × 𝐂
→ 𝟔𝟔 × 𝐒 = 𝟖𝟖 × 𝐂
→ 𝐒: 𝐂 = 𝟖𝟖: 𝟔𝟔 = 𝟒: 𝟑
𝟏
𝟏
∴ %𝐏 = (𝟑 × 𝟏𝟎𝟎) % = 𝟑𝟑 𝟑 %
Short Trick:
Sol:
𝐒𝐏 ∶ 𝐂𝐏 = (𝟔𝟔 + 𝟐𝟐) ∶ 𝟔𝟔
= 𝟖𝟖 ∶ 𝟔𝟔
= 4:3
𝟏
𝟏
%𝐏 = (𝟑 × 𝟏𝟎𝟎) % = 𝟑𝟑 𝟑 %
Page 19 of 33
Q.11: A man sold 17 balls for Rs.720 and loses the cost price of 5 balls.
Find the cost price of one ball.
Sol: Let C and S be the cost price and the selling price of one ball; respectively.
𝐂𝐏 − 𝐒𝐏 = 𝐋
→ 𝟏𝟕 × 𝐂 − 𝟏𝟕 × 𝐒 = 𝟓 × 𝐂
→ 𝟏𝟐 × 𝐂 = 𝟏𝟕 × 𝐒
→ 𝟏𝟐 × 𝐂 = 𝐑𝐬. 𝟕𝟐𝟎
→ 𝟏 × 𝐂 = 𝐑𝐬. 𝟔𝟎 ≡ 𝐂𝐨𝐬𝐭 𝐏𝐫𝐢𝐜𝐞 𝐨𝐟 𝟏 𝐁𝐚𝐥𝐥
Q.12: A shopkeeper sold an article at a certain price. If he sold it at 𝟐⁄𝟑
of that price; he loses 10%. What would be his profit percentage; if he
sold it at the original price?
Sol:
Let S be the original selling price.
𝟐
𝟑
× 𝑺 ≡ 𝟗𝟎%
𝟑
→ 𝑺 ≡ 𝟗𝟎% × 𝟐 = 𝟏𝟑𝟓%
∴ %𝑷 = 𝟏𝟑𝟓% − 𝟏𝟎𝟎% = 𝟑𝟓%
Q.13: If the selling price of an article is reduced by 60%; then there is a
loss of 10% on cost price. What was initial profit percentage?
Sol:
Let S be the original selling price.
𝟒𝟎
𝟏𝟎𝟎
× 𝑺 ≡ 𝟗𝟎%
→ 𝑺 ≡ 𝟗𝟎% ×
𝟏𝟎𝟎
𝟒𝟎
= 𝟐𝟐𝟓%
∴ %𝑷 = 𝟐𝟐𝟓% − 𝟏𝟎𝟎% = 𝟏𝟐𝟓%
Page 20 of 33
Q.14: If the selling price of an article is reduced to 60%; then there is a
loss of 10% on cost price. What was initial profit percentage?
Sol:
Let S be the original selling price.
𝟔𝟎
𝟏𝟎𝟎
× 𝑺 ≡ 𝟗𝟎%
→ 𝑺 ≡ 𝟗𝟎% ×
𝟏𝟎𝟎
𝟔𝟎
= 𝟏𝟓𝟎%
∴ %𝑷 = 𝟏𝟓𝟎% − 𝟏𝟎𝟎% = 𝟓𝟎%
The relation between the Cost Price, Marked up Price and Selling Price:
Q.1: A shopkeeper marks the price of his goods by increasing 25%. On
𝟏
cash payment he allows a discount of 𝟏𝟐 𝟐 % to the customer. Find his
net profit percentage in the deal.
Page 21 of 33
P%
Sol:
Sol:
CP
𝟐𝟓%+
𝟏
𝟏𝟐 𝟐 %−
MP
SP
𝟏
𝟏 𝟐𝟓 × 𝟏𝟐 𝟐
%𝑷 = 𝟐𝟓 − 𝟏𝟐 −
𝟐
𝟏𝟎𝟎
𝟑
∴ %𝑷 = 𝟗 𝟖 %
Q.2: On cash payment a shopkeeper allows a discount of 5%. At what
percentage above cost price should he mark it up in order to gain 10%?
𝟏𝟎%+
Sol:
Sol: CP
𝒙%+
𝟓%−
MP
𝟏𝟎 = 𝒙 − 𝟓 −
SP
𝒙×𝟓
𝟏𝟎𝟎
𝟏𝟓
∴ 𝒙 = 𝟏𝟓 𝟏𝟗 %
Q.3: A profit of 20% is made when a discount of 10% is given. What
would be the profit percentage if:
1) The discount is increase to 20%
2) No discount is offered.
Page 22 of 33
Sol.1:
Sol.1: CP
𝟐𝟎%+
𝒙%+
%𝐏 =?
MP
𝟐𝟎 = 𝐱 − 𝟏𝟎 −
𝟏𝟎%−
𝐱 × 𝟏𝟎
𝟏𝟎𝟎
∴𝐱=
Sol.2:
Sol.2: CP
SP
𝟏𝟎𝟎
𝟑
Sol.1: CP
𝟏𝟎𝟎
𝟑
MP
𝟐𝟎 = 𝐱 − 𝟏𝟎 −
∴𝐱=
𝟏𝟎𝟎
𝟑
%
MP 𝟐𝟎%−
SP
𝟏𝟎𝟎
× 𝟐𝟎
𝟏𝟎𝟎
%𝐏 =
− 𝟐𝟎 − 𝟑
𝟑
𝟏𝟎𝟎
%
𝟐
∴ %𝐏 = 𝟔 %
𝟑
𝟐𝟎%+
𝒙%+
%+
%𝐏 =?
𝟏𝟎%−
𝐱 × 𝟏𝟎
𝟏𝟎𝟎
SP
Sol.2: CP
𝟏𝟎𝟎
𝟑
%+
MP 𝟎%−
SP
𝟏𝟎𝟎
×𝟎
𝟏𝟎𝟎
%𝐏 =
−𝟎− 𝟑
𝟑
𝟏𝟎𝟎
𝟏
∴ %𝐏 = 𝟑𝟑 %
𝟑
Q.4: A man marks his article such that he can make 32% profit after
giving 12% discount. However a customer availed 20% discount
instead of 12%. What is the new profit% on article?
Page 23 of 33
𝟑𝟐%+
Sol:
Sol: CP
𝒙%+
MP
%𝐏 =?
𝟏𝟐%−
𝟑𝟐 = 𝐱 − 𝟏𝟐 −
SP
Sol:
CP
𝐱×𝟏𝟐
𝟏𝟎𝟎
𝟓𝟎%+
MP
%𝐏 = 𝟓𝟎 − 𝟐𝟎 −
∴ 𝐱 = 𝟓𝟎%
𝟐𝟎%−
SP
𝟓𝟎 × 𝟐𝟎
𝟏𝟎𝟎
∴ %𝐏 = 𝟐𝟎%
Q.5: A shopkeeper bought a refrigerator for Rs.18000. At what price
should he mark it in order to gain 30% after giving a discount of 10%?
𝟑𝟎%+
Sol:
Sol: 𝐂𝐏 = 𝐑𝐬. 𝟏𝟖𝟎𝟎𝟎 𝐌𝐏 =?
𝟏𝟎%−
SP
𝑹𝒔. 𝟏𝟖𝟎𝟎𝟎
(
𝟏𝟎𝟎% × 𝟏𝟑𝟎%)
𝑴𝑷 =
× 𝟏𝟎𝟎%
𝟗𝟎%
= 𝑹𝒔. 𝟐𝟔𝟎𝟎𝟎
Q.6: A shopkeeper marks the price of his goods at Rs.2750. He allows a
discount of 5% to the customers while selling. His net profit is 4.5%.
Find at what price did he bought the article?
Page 24 of 33
Net Profit= 𝟒. 𝟓%+
Sol:
Sol: 𝐂𝐏 =?
𝐌𝐏 = 𝐑𝐬. 𝟐𝟕𝟓𝟎
𝟓%−
𝐒𝐏
𝑹𝒔. 𝟐𝟕𝟓𝟎
(
𝟏𝟎𝟎% × 𝟗𝟓%)
𝑪𝑷 =
× 𝟏𝟎𝟎%
𝟏𝟎𝟒. 𝟓%
= 𝑹𝒔. 𝟐𝟓𝟎𝟎
Q.7: A shopkeeper allows 23% commission on his marked price and still
makes a profit of 10%.if he gains Rs.56 on the item. Find the marked
price of the item?
𝟏𝟎%+ ≡ 𝑹𝒔. 𝟓𝟔
Sol:
Sol: 𝐂𝐏
𝐋𝐞𝐭 𝐌𝐏 = 𝟏𝟎𝟎%
𝑫, 𝟐𝟑%−
𝐒𝐏, 10% P
𝑹𝒔. 𝟓𝟔
(
𝟏𝟎% × 𝟏𝟏𝟎%)
𝑴𝑷 =
× 𝟏𝟎𝟎%
𝟕𝟕%
= 𝑹𝒔. 𝟖𝟎𝟎
Q.8: A shopkeeper marks an article at Rs.60 and sells it at a discount of
15%. He also gives a gifts worth Rs.3. If he still makes 20% profit; find
the cost price?
Page 25 of 33
𝟐𝟎%+
Sol:
Sol: 𝐂𝐏 =?
𝐌𝐏 = 𝐑𝐬. 𝟔𝟎
𝟏𝟓%− SP + Rs.3
𝑹𝒔. 𝟔𝟎
𝟏𝟎𝟎% × 𝟗𝟓% + 𝑹𝒔. 𝟑)
𝑪𝑷 =
× 𝟏𝟎𝟎%
𝟏𝟐𝟎%
(
= 𝑹𝒔. 𝟓𝟎
Miscellaneous Questions
Q.1: A man bought 30 toffees for a rupee. How many toffees
for a rupee should he sell in order to gain 25%?
Short Trick:
𝟏𝟎𝟎
Sol: = 𝟑𝟎 × 𝟏𝟐𝟓
= 𝟐𝟒 𝐭𝐨𝐟𝐟𝐞𝐞𝐬
Q.2: A man bought 30 toffees for Rs.12. How many toffees for
Rs.13 should he sell in order to gain 25%?
Short Trick:
𝟑𝟎
𝟏𝟎𝟎
Sol: = 𝟏𝟐 × 𝟏𝟐𝟓 × 𝟏𝟑
= 𝟐𝟔 𝐭𝐨𝐟𝐟𝐞𝐞𝐬
Page 26 of 33
Q.3: A man sold 18 apples for a rupee and losses 40%. How
many apples for a rupee should he sell in order to gain 20%?
Short Trick:
𝟔𝟎
𝟏𝟎𝟎
Sol: = 𝟏𝟖 × 𝟏𝟎𝟎 × 𝟏𝟐𝟎
= 𝟗 𝐚𝐩𝐩𝐥𝐞𝐬
Q.4: A man sold 18 apples for Rs.90 and losses 40%. How many
apples for Rs.130 should he sell in order to gain 20%?
Short Trick:
𝟏𝟖
𝟔𝟎
𝟏𝟎𝟎
Sol: = 𝟗𝟎 × 𝟏𝟎𝟎 × 𝟏𝟐𝟎 × 𝟏𝟑𝟎
= 𝟏𝟑 𝐚𝐩𝐩𝐥𝐞𝐬
Q.5: A boy buys apples at 9 for Rs.16 and sells them at 11 for
Rs.20. what does his gain or lose percentage?
𝑨𝒓𝒕𝒊𝒄𝒍𝒆𝒔
𝑹𝒔.
𝑪𝑷
𝒏
𝒂
𝑺𝑷
𝒎
𝒃
Page 27 of 33
𝑻𝒉𝒆𝒏 %𝑷 𝒐𝒓 %𝑳 = (
𝒏𝒃 − 𝒎𝒂
× 𝟏𝟎𝟎) %
𝒎𝒂
Note: If sign comes out to be (+) ve, then profit and if (-) ve, then loss.
Hence
∴
𝑨𝒓𝒕𝒊𝒄𝒍𝒆𝒔
𝑹𝒔.
𝑪𝑷
𝟗
𝟏𝟔
𝑺𝑷
𝟏𝟏
𝟐𝟎
𝟗 × 𝟐𝟎 − 𝟏𝟏 × 𝟏𝟔
𝟑
× 𝟏𝟎𝟎 = +𝟐
% ← 𝐏𝐫𝐨𝐟𝐢𝐭
𝟏𝟏 × 𝟏𝟔
𝟏𝟏
Q.6: A machine is sold for Rs.5060 at a gain of 10%. What would
have been the gain or loss percentage if it had been sold for
Rs.4370?
Short Trick:
𝟏𝟏𝟎%
Sol: = 𝐑𝐬.𝟓𝟎𝟔𝟎
× 𝐑𝐬. 𝟒𝟑𝟕𝟎
= 𝟗𝟓% < 𝟏𝟎𝟎%(𝐂𝐏)
∴ %𝐋 = 𝟓%
Page 28 of 33
Q.7: The profit earned by selling an article for Rs.900 is 100%
more than the loss incurred when the same article is sold for
Rs.450. at what price should the article be sold to make 25%
profit?
Sol: Cost price never changes on changing the selling price. As when
selling price changes; profit/loss accordingly changes to nullify the
change.
Short Trick:
Sol:
𝟐𝟎𝟎
∴ (𝟗𝟎𝟎 − 𝐂) = 𝟏𝟎𝟎 (𝐂 − 𝟒𝟓𝟎)
→ 𝑪 = 𝑹𝒔. 𝟔𝟎𝟎
Hence; 𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐒𝐏 =
𝐑𝐬.𝟔𝟎𝟎
𝟏𝟎𝟎%
× 𝟏𝟐𝟓% = 𝐑𝐬. 𝟕𝟓𝟎
Q.8: Manju sells an article to Anju at a profit of 25%. Anju sells
it to Sonia at a gain of 10% and Sonia sells it to Bobby at a profit
of 5%. If Sonia sells it for Rs.231, find the cost price at which
Manju bought the article?
Short Trick:
Sol:
Manju
+𝟏
𝟒
Anju
𝑹𝒔.𝟐𝟑𝟏
𝑪𝑷 𝒇𝒐𝒓 𝑴𝒂𝒏𝒋𝒖 = 𝟐𝟏×𝟏𝟏×𝟓
= 𝑹𝒔. 𝟏𝟔𝟎
+𝟏
𝟏𝟎
+𝟏
Sonia
Bobby
𝟐𝟎
 CP = Rs.231
× (𝟐𝟎 × 𝟏𝟎 × 𝟒)
Page 29 of 33
Q.9: A man sold an article at a profit of 10%. If he bought it at
10% less and sold for Rs.18 more; he gains 25%. Find the cost
price of the article?
−𝟏𝟎 + 𝟐𝟓 −
Sol:
𝟏𝟎×𝟐𝟓
𝟏𝟎𝟎
= 𝟏𝟐. 𝟓%
Short Trick:
Wholesaler
Retailer
𝟏𝟎%+
Customer
𝑹𝒔.𝟏𝟖
Hence; 𝑪𝑷 = (𝟏𝟐.𝟓−𝟏𝟎)% × 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟕𝟐𝟎
Q.10: The cost price of an article is 𝟐⁄𝟑 𝒓𝒅 of its marked price
and the marked price is 𝟒⁄𝟑 𝒓𝒅 of the selling price. Find the
profit percentage.
Short Trick:
𝑪𝑷 :
𝑴𝑷 =
𝟐 : 𝟑
𝑴𝑷 :
𝑺𝑷 =
𝟒 : 𝟑
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆; 𝑪𝑷 : 𝑴𝑷 : 𝑺𝑷 = 𝟖 : 𝟏𝟐 : 𝟗
𝟏
𝑯𝒆𝒏𝒄𝒆;
%𝑷 = 𝟖 × 𝟏𝟎𝟎
= 𝟏𝟐. 𝟓%
Sol:
Page 30 of 33
Q.11: A retailer got a discount of 10% on the marked price of a
watch from the whole seller. In turn he sells it at marked price.
Find his gain percentage.
Short Trick:
Sol:
𝐌𝐏 ∶
=
=
𝐂𝐏
𝟏𝟎𝟎
∶
𝟗𝟎
𝟏𝟎
∶
𝟗
∶
𝐒𝐏
∶
∶
𝟏𝟎𝟎
𝟏𝟎
𝟏
%𝐏 = (𝟗 × 𝟏𝟎𝟎) %
Hence;
𝟏
= 𝟏𝟏 𝟗 %
Q.12: Monica purchased a pressure cooker at 9/10 of its selling price
and sold it at 8% more than its selling price. Find her gain percentage.
Short Trick:
Sol:
𝐒𝐏(𝐒𝐡𝐨𝐩𝐤𝐞𝐞𝐩𝐞𝐫) ∶ 𝐂𝐏(𝐌𝐨𝐧𝐢𝐜𝐚) ∶
Hence;
=
𝟏𝟎𝟎
=
𝟓𝟎
∶
𝟗𝟎
∶
𝟒𝟓
%𝐏(𝐌𝐨𝐧𝐢𝐜𝐚) = (
𝟗
𝟒𝟓
𝐒𝐏(𝐌𝐨𝐧𝐢𝐜𝐚)
∶
𝟏𝟎𝟖
∶
𝟓𝟒
× 𝟏𝟎𝟎) %
= 𝟐𝟎%
Q.13: An article is sold at 20% profit. If its CP and SP are less by Rs.10
and Rs.5 respectively, the percentage profit increases by 10%. Find the
cost price.
Page 31 of 33
Short Trick:
Sol:
=
𝑹𝒔.𝟏𝟎
×𝟏𝟑𝟎%−𝑹𝒔.𝟓
𝟏𝟎𝟎%
𝟏𝟎%
× 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟖𝟎
myshop.mahendras.org
Page 32 of 33
Q.14: An article is sold at 25% profit if its CP and SP are more by Rs.20
and Rs.4 respectively, the percentage of profit decreases by 15%. Find
the cost price
Short Trick:
Sol:
=
𝑹𝒔.𝟐𝟎
×𝟏𝟏𝟎%+𝑹𝒔.𝟒
𝟏𝟎𝟎%
−
−𝟏𝟓%
× 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟏𝟐𝟎
Q.15: An article is sold at 20% profit. If its CP and SP are Rs.100 less, the
percentage profit would be 4% more. Find the cost price.
Short Trick:
Sol:
=
𝑹𝒔.𝟏𝟎𝟎
×𝟏𝟐𝟒%−𝑹𝒔.𝟏𝟎𝟎
𝟏𝟎𝟎%
𝟒%
× 𝟏𝟎𝟎%
= 𝑹𝒔. 𝟔𝟎𝟎
www.bankersguru.org
Page 33 of 33