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Page 2 of 33
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 bestโฆ
Page 3 of 33
Contents
1. Preface โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ..โฆโฆโฆโฆโฆโฆโฆ 2
2. Contents โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ 3
3. Introduction โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ 4
4. Concept of Cost Price, Selling Price and Marked Price ...โฆโฆโฆ4
5. Strategy..โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ. 8
6. Questions Based on Application of Unitary Method โฆโฆโฆ......9
7. How to Calculate the Percentage Profit/ Percentage Loss ....15
8. The Relation Between Cost Price, Marked Up Price
And Selling Price ...โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ.โฆโฆ.21
9. Miscellaneous Questions โฆโฆโฆโฆโฆโฆโฆโฆโฆโฆ.โฆโฆโฆโฆโฆโฆ..โฆ.โฆ.26
Page 4 of 33
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?
Page 5 of 33
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; whyโฆ! 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.
๐ท๐๐๐๐๐ = ๐บ๐๐๐๐๐๐ ๐ท๐๐๐๐ โ ๐ช๐๐๐ ๐ท๐๐๐๐
Page 6 of 33
(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; whyโฆ! 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.
(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. OKโฆ.!!! We concluded an important pointโฆโฆ 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)
๐ณ๐๐๐ = ๐ช๐๐๐ ๐ท๐๐๐๐ โ ๐บ๐๐๐๐๐๐ ๐ท๐๐๐๐
๐บ๐๐๐๐๐๐ ๐ท๐๐๐๐
๐ช๐๐๐ ๐ท๐๐๐๐
๐๐จ๐ฌ๐ฌ
๐๐ซ๐จ๐๐ข๐ญ
๐บ๐๐๐๐๐๐ ๐ท๐๐๐๐
๐๐ > CP
๐๐ < CP
Page 7 of 33
2. Now we could easily digest the following two points for handling the question
i. In case of Profit:
ii. In case of Loss:
% P = 10%
๐๐ = 110%
๐๐ = 100%
% L = 20%
๐๐ = 80%
๐๐ = 100%
๐ช๐๐๐ ๐ท๐๐๐๐ = 100%
๐ณ๐๐๐
๐ท๐๐๐๐๐
(๐ฉ๐๐๐ ๐๐๐๐๐)
Page 8 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.
Strategy:
In forthcoming discussion what we are going to doโฆ..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
% D = 30%
๐๐ = 70%
๐๐ = 100%
๐๐ = 100%
๐บ๐๐๐๐๐๐ ๐ท๐๐๐๐
(Base value)
Discount
Page 9 of 33
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:
Q.1: A man bought an article for Rs.425. For how much should he sell it
in order to gain 8%?
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%?
๐ฝ๐๐๐๐
๐ฌ๐๐๐๐๐๐๐๐๐ ๐ท๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐ร ๐ท๐๐๐๐๐๐๐๐๐ ๐ฝ๐๐๐๐ ๐๐๐๐๐ ๐๐ ๐จ๐๐๐๐
Short Trick:
Sol: = ๐น๐.๐๐๐
๐๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐
Page 10 of 33
Q.3: A fruit seller sold the fruits for Rs.3900 and gains 20%. Find at what
price did he bought the fruits?
Q.4: I sold a book for Rs.705.76, and loosed 12%. Find the cost price of
the book.
Q.5: A man sold an article for Rs.250 and thereby gain 25%. Find how
much amount did he gains?
Short Trick:
Sol: = ๐น๐.๐๐๐๐
๐๐๐%ร ๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: =
๐น๐.๐๐๐๐
๐๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐.๐๐
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐
Short Trick:
Sol: = ๐น๐.๐๐๐
๐๐๐%ร ๐๐%
= ๐น๐. ๐๐
Page 11 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?
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?
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%?
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:
Sol: = ๐น๐.๐๐๐
๐.๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐
๐%ร ๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐๐
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐
๐๐๐%ร (๐๐๐% โ ๐๐๐%)
= ๐น๐. ๐๐
Page 12 of 33
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?
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?
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?
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: Sol: = ๐น๐.๐๐
๐๐%โ๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐
Short Trick: Sol: = ๐น๐.๐๐
(โ๐)%โ(โ๐)%ร ๐๐๐%
= ๐น๐. ๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐
๐๐%โ(โ๐)%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐
๐.๐%โ(โ๐.๐)%ร ๐๐๐. ๐%
= Rs.1125
Page 13 of 33
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?
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.
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?
Q.17: Find the single discount of three successive discount of 10%, 20%
and 30%?
Short Trick: Sol: = ๐น๐.๐๐๐๐
๐๐%ร ๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐๐
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Short Trick: Sol: = ๐น๐.๐๐๐
๐๐%โ๐๐%ร ๐๐%
= ๐น๐. ๐๐๐๐
Page 14 of 33
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?
Q.19: What is the difference between a 45% discount on Rs.1000 and
successive discounts of 30% and 10% on the same amount?
How to Calculate the Percentage Profit/ Percentage Loss/Percentage Discount:
Short Trick: Sol: ๐๐๐ญ ๐๐ข๐ฌ๐๐จ๐ฎ๐ง๐ญ
= ๐๐๐ญ ๐๐๐๐๐๐ญ(๐๐%โ, ๐๐%โ, ๐๐%โ)
= โ๐๐. ๐%
Short Trick: Sol:
Rs.16000 ๐%โ ๐๐๐๐๐
๐๐๐%ร ๐๐% = ๐น๐. ๐๐๐๐๐ ๐ฟ%
- Rs.11400
๐ฟ =๐๐๐๐๐ โ ๐๐๐๐๐
๐๐๐๐๐ร ๐๐๐ = โ๐๐ = ๐๐% ๐ซ๐๐๐๐๐๐๐
Short Trick: Sol: ๐๐๐ญ ๐๐ข๐ฌ๐๐จ๐ฎ๐ง๐ญ
= โ๐๐ โ ๐๐ +๐๐ ร ๐๐
๐๐๐= โ๐๐%
๐๐๐ช๐ฎ๐ข๐ซ๐๐ ๐๐ข๐๐๐๐ซ๐๐ง๐๐
=๐๐ฌ. ๐๐๐๐
๐๐๐%ร (๐๐ โ ๐๐)%
= ๐๐ฌ. ๐๐
Page 15 of 33
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 โcost price; whether it is the exact valued or the relative valuedโ
(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 โ%โ sign after that (just to nullify the multiplication by 100,
its equivalent โ% โก๐
๐๐๐โ 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.
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
Short Trick:
Sol: %๐ =๐๐ฌ.๐๐๐๐โ(๐๐ฌ.๐๐๐๐+๐๐ฌ.๐๐๐)
๐๐ฌ.๐๐๐๐+๐๐ฌ.๐๐๐ร ๐๐๐
= ๐๐
๐๐%
Page 16 of 33
1) The profit percentage of the shopkeeper.
2) The loss percentage of the customer.
Q.3: The cost price of an article is ๐ ๐โ๐๐
of the selling price. Find the
percentage profit or the percentage loss.
Q.4: The profit earned by selling an article is ๐๐๐
๐% of the selling price.
Find the percentage profit.
Short Trick: Sol.1: %๐ =
๐๐๐ ๐ ๐ฆ
๐๐๐ ๐ ๐ฆร ๐๐๐
= ๐๐๐
๐%
Short Trick: Sol.2: %๐ =
๐๐๐ ๐ ๐ฆ
๐๐๐๐ ๐ ๐ฆร ๐๐๐
= ๐๐%
Short Trick: Sol: ๐๐ โถ ๐๐ = ๐: ๐
โด %๐ = (๐
๐ร ๐๐๐) %
= ๐๐%
Page 17 of 33
Q.5: 20% profit on selling price is what percent profit on cost price?
Q.6: 10% loss on cost price is what percent loss on selling price?
Q.7: If the selling price is tripled; the profit becomes four times; find
the percentage profit on the actual selling price?
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: ๐๐
๐
๐% โก
๐
๐
๐: ๐๐ = ๐: ๐
%๐ = (๐
๐ร ๐๐๐) % = ๐๐%
Short Trick: Sol: ๐ โถ ๐๐ = ๐๐ โถ ๐๐๐
= ๐ โถ ๐
%๐ = (๐
๐ร ๐๐๐) % = ๐๐%
Short Trick: Sol: ๐ โถ ๐๐ = ๐๐ โถ ๐๐๐
= ๐ โถ ๐๐
%๐ = (๐
๐ร ๐๐๐) % = ๐๐
๐
๐%
Page 18 of 33
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.
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.
๐๐ โ ๐๐ = ๐
โ ๐๐ ร ๐ โ ๐๐ ร ๐ = ๐๐ ร ๐
โ ๐๐ ร ๐ = ๐๐ ร ๐
โ ๐: ๐ = ๐๐: ๐๐ = ๐: ๐
If S be the original selling price and P be
the original profit.
๐ โ ๐ = ๐ ร ๐ โ ๐ ร ๐
โ ๐ ร ๐๐ = ๐ ร ๐
โ ๐๐: ๐ = ๐: ๐
โด %๐ =๐
๐ร ๐๐๐ = ๐๐๐%
๐๐ ร ๐ = ๐ ร ๐
โ ๐๐: ๐๐ = ๐: ๐๐
โด %๐ = (๐
๐ร ๐๐๐) %
= ๐๐๐
๐%
Page 19 of 33
โด %๐ = (๐
๐ร ๐๐๐) % = ๐๐%
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.
๐๐ โ ๐๐ = ๐
โ ๐๐ ร ๐ โ ๐๐ ร ๐ = ๐๐ ร ๐
โ ๐๐ ร ๐ = ๐๐ ร ๐
โ ๐: ๐ = ๐๐: ๐๐ = ๐: ๐
โด %๐ = (๐
๐ร ๐๐๐) % = ๐๐
๐
๐%
Short Trick: Sol: ๐ โถ ๐๐ = ๐๐ โถ (๐๐ โ ๐๐)
= ๐๐ โถ ๐๐
= 1 : 2
%๐ = (๐
๐ร ๐๐๐) % = ๐๐%
Short Trick: Sol: ๐๐ โถ ๐๐ = (๐๐ + ๐๐) โถ ๐๐
= ๐๐ โถ ๐๐
= 4 : 3
%๐ = (๐
๐ร ๐๐๐) % = ๐๐
๐
๐%
Page 20 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.
Q.12: A shopkeeper sold an article at a certain price. If he sold it at ๐ ๐โ
of that price; he loses 10%. What would be his profit percentage; if he
sold it at the original price?
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?
๐๐ โ ๐๐ = ๐
โ ๐๐ ร ๐ โ ๐๐ ร ๐ = ๐ ร ๐
โ ๐๐ ร ๐ = ๐๐ ร ๐
โ ๐๐ ร ๐ = ๐๐ฌ. ๐๐๐
โ ๐ ร ๐ = ๐๐ฌ. ๐๐ โก ๐๐จ๐ฌ๐ญ ๐๐ซ๐ข๐๐ ๐จ๐ ๐ ๐๐๐ฅ๐ฅ
Sol: Let S be the original selling price.
๐
๐ร ๐บ โก ๐๐%
โ ๐บ โก ๐๐% ร๐
๐= ๐๐๐%
โด %๐ท = ๐๐๐% โ ๐๐๐% = ๐๐%
Sol: Let S be the original selling price.
๐๐
๐๐๐ร ๐บ โก ๐๐%
โ ๐บ โก ๐๐% ร๐๐๐
๐๐= ๐๐๐%
โด %๐ท = ๐๐๐% โ ๐๐๐% = ๐๐๐%
Page 21 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?
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
cash payment he allows a discount of ๐๐๐
๐% to the customer. Find his
net profit percentage in the deal.
Sol: P%
Sol: Let S be the original selling price.
๐๐
๐๐๐ร ๐บ โก ๐๐%
โ ๐บ โก ๐๐% ร๐๐๐
๐๐= ๐๐๐%
โด %๐ท = ๐๐๐% โ ๐๐๐% = ๐๐%
Page 22 of 33
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%?
Sol: ๐๐%+
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.
Sol.1: ๐๐%+ %๐ =?
Sol: CP ๐๐%+ MP ๐๐๐
๐%โ SP
%๐ท = ๐๐ โ ๐๐๐
๐โ
๐๐ ร ๐๐๐๐
๐๐๐
โด %๐ท = ๐๐
๐%
Sol: CP ๐%+ MP ๐%โ SP
๐๐ = ๐ โ ๐ โ๐ ร ๐
๐๐๐
โด ๐ = ๐๐๐๐
๐๐%
Page 23 of 33
Sol.2: ๐๐%+ %๐ =?
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?
Sol.1: CP ๐%+ MP ๐๐%โ SP
๐๐ = ๐ฑ โ ๐๐ โ๐ฑ ร ๐๐
๐๐๐
โด ๐ฑ =๐๐๐
๐%
Sol.1: CP ๐๐๐
๐%+ MP ๐๐%โ SP
%๐ =๐๐๐
๐โ ๐๐ โ
๐๐๐๐ ร ๐๐
๐๐๐
โด %๐ = ๐๐
๐%
Sol.2: CP ๐%+ MP ๐๐%โ SP
๐๐ = ๐ฑ โ ๐๐ โ๐ฑ ร ๐๐
๐๐๐
โด ๐ฑ =๐๐๐
๐%
Sol.2: CP ๐๐๐
๐%+ MP ๐%โ SP
%๐ =๐๐๐
๐โ ๐ โ
๐๐๐๐ ร ๐
๐๐๐
โด %๐ = ๐๐๐
๐%
Page 24 of 33
Sol: ๐๐%+ %๐ =?
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%?
Sol: ๐๐%+
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?
Sol: Net Profit= ๐. ๐%+
Sol: CP ๐%+ MP ๐๐%โ SP
๐๐ = ๐ฑ โ ๐๐ โ๐ฑร๐๐
๐๐๐
โด ๐ฑ = ๐๐%
Sol: CP ๐๐%+ MP ๐๐%โ SP
%๐ = ๐๐ โ ๐๐ โ๐๐ ร ๐๐
๐๐๐
โด %๐ = ๐๐%
Sol: ๐๐ = ๐๐ฌ. ๐๐๐๐๐ ๐๐ =? ๐๐%โ SP
๐ด๐ท =(
๐น๐. ๐๐๐๐๐๐๐๐% ร ๐๐๐%)
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐๐
Page 25 of 33
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?
Sol: ๐๐%+ โก ๐น๐. ๐๐
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?
Sol: ๐๐%+
Sol: ๐๐ =? ๐๐ = ๐๐ฌ. ๐๐๐๐ ๐%โ ๐๐
๐ช๐ท =(
๐น๐. ๐๐๐๐๐๐๐% ร ๐๐%)
๐๐๐. ๐%ร ๐๐๐%
= ๐น๐. ๐๐๐๐
Sol: ๐๐ ๐๐๐ญ ๐๐ = ๐๐๐% ๐ซ, ๐๐%โ ๐๐, 10% P
๐ด๐ท =(
๐น๐. ๐๐๐๐% ร ๐๐๐%)
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐
Page 26 of 33
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%?
Q.2: A man bought 30 toffees for Rs.12. How many toffees for
Rs.13 should he sell in order to gain 25%?
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%?
Sol: ๐๐ =? ๐๐ = ๐๐ฌ. ๐๐ ๐๐%โ SP + Rs.3
๐ช๐ท =(
๐น๐. ๐๐๐๐๐% ร ๐๐% + ๐น๐. ๐)
๐๐๐%ร ๐๐๐%
= ๐น๐. ๐๐
Short Trick: Sol: = ๐๐ ร
๐๐๐
๐๐๐
= ๐๐ ๐ญ๐จ๐๐๐๐๐ฌ
Short Trick: Sol: = ๐๐
๐๐ร
๐๐๐
๐๐๐ร ๐๐
= ๐๐ ๐ญ๐จ๐๐๐๐๐ฌ
Page 27 of 33
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%?
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?
Short Trick: Sol: = ๐๐ ร
๐๐
๐๐๐ร
๐๐๐
๐๐๐
= ๐ ๐๐ฉ๐ฉ๐ฅ๐๐ฌ
Short Trick: Sol: = ๐๐
๐๐ร
๐๐
๐๐๐ร
๐๐๐
๐๐๐ร ๐๐๐
= ๐๐ ๐๐ฉ๐ฉ๐ฅ๐๐ฌ
๐ช๐ท
๐บ๐ท
๐จ๐๐๐๐๐๐๐ ๐น๐.
๐
๐ ๐
๐
๐ป๐๐๐ %๐ท ๐๐ %๐ณ = (๐๐ โ ๐๐
๐๐ร ๐๐๐) %
Page 28 of 33
Note: If sign comes out to be (+) ve, then profit and if (-) ve, then loss.
Hence
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?
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
โด๐ ร ๐๐ โ ๐๐ ร ๐๐
๐๐ ร ๐๐ร ๐๐๐ = +๐
๐
๐๐% โ ๐๐ซ๐จ๐๐ข๐ญ
๐ช๐ท
๐บ๐ท
๐จ๐๐๐๐๐๐๐ ๐น๐.
๐๐
๐๐ ๐๐
๐
Short Trick: Sol: = ๐๐๐%
๐๐ฌ.๐๐๐๐ร ๐๐ฌ. ๐๐๐๐
= ๐๐% < ๐๐๐%(๐๐)
โด %๐ = ๐%
Page 29 of 33
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.
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:
โด (๐๐๐ โ ๐) =๐๐๐
๐๐๐(๐ โ ๐๐๐)
โ ๐ช = ๐น๐. ๐๐๐
Hence; ๐๐๐ช๐ฎ๐ข๐ซ๐๐ ๐๐ =๐๐ฌ.๐๐๐
๐๐๐%ร ๐๐๐% = ๐๐ฌ. ๐๐๐
Short Trick: Sol:
Manju +๐
๐ Anju
+๐
๐๐ Sonia
+๐
๐๐ Bobby
CP = Rs.231
๐ช๐ท ๐๐๐ ๐ด๐๐๐๐ =๐น๐.๐๐๐
๐๐ร๐๐ร๐ร (๐๐ ร ๐๐ ร ๐)
= ๐น๐. ๐๐๐
Page 30 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?
Sol: โ๐๐ + ๐๐ โ๐๐ร๐๐
๐๐๐= ๐๐. ๐%
Q.10: The cost price of an article is ๐ ๐โ ๐๐ of its marked price
and the marked price is ๐๐โ ๐๐ of the selling price. Find the
profit percentage.
Short Trick: Wholesaler Retailer ๐๐%+ Customer
Hence; ๐ช๐ท =๐น๐.๐๐
(๐๐.๐โ๐๐)%ร ๐๐๐%
= ๐น๐. ๐๐๐
Short Trick: Sol: ๐ช๐ท : ๐ด๐ท = ๐ : ๐
๐ด๐ท : ๐บ๐ท = ๐ : ๐
๐ป๐๐๐๐๐๐๐๐; ๐ช๐ท : ๐ด๐ท : ๐บ๐ท = ๐ : ๐๐ : ๐
๐ฏ๐๐๐๐; %๐ท =๐
๐ร ๐๐๐
= ๐๐. ๐%
Page 31 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.
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.
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.
Short Trick: Sol: ๐๐ โถ ๐๐ โถ ๐๐
= ๐๐๐ โถ ๐๐ โถ ๐๐๐
= ๐๐ โถ ๐ โถ ๐๐
Hence; %๐ = (๐
๐ร ๐๐๐) %
= ๐๐๐
๐%
Short Trick: Sol: ๐๐(๐๐ก๐จ๐ฉ๐ค๐๐๐ฉ๐๐ซ) โถ ๐๐(๐๐จ๐ง๐ข๐๐) โถ ๐๐(๐๐จ๐ง๐ข๐๐)
= ๐๐๐ โถ ๐๐ โถ ๐๐๐
= ๐๐ โถ ๐๐ โถ ๐๐
Hence; %๐(๐๐จ๐ง๐ข๐๐) = (๐
๐๐ร ๐๐๐) %
= ๐๐%
Page 32 of 33
Short Trick: Sol:
= ๐น๐.๐๐
๐๐๐%ร๐๐๐%โ๐น๐.๐
๐๐%ร ๐๐๐%
= ๐น๐. ๐๐
myshop.mahendras.org
Page 33 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
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: = โ
๐น๐.๐๐
๐๐๐%ร๐๐๐%+๐น๐.๐
โ๐๐%ร ๐๐๐%
= ๐น๐. ๐๐๐
Short Trick:
Sol: = ๐น๐.๐๐๐
๐๐๐%ร๐๐๐%โ๐น๐.๐๐๐
๐%ร ๐๐๐%
= ๐น๐. ๐๐๐