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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.

𝑷𝒓𝒐𝒇𝒊𝒕 = 𝑺𝒆𝒆𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆 − 𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆

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(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.

(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)

𝑳𝒐𝒔𝒔 = 𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆 − 𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆

𝑺𝒆𝒍𝒍𝒊𝒏𝒈 𝑷𝒓𝒊𝒄𝒆

𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆

𝐋𝐨𝐬𝐬

𝐏𝐫𝐨𝐟𝐢𝐭


𝐒𝐏 > CP

𝐒𝐏 < CP

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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%

𝐒𝐏 = 110%

𝐂𝐏 = 100%

% L = 20%

𝐒𝐏 = 80%

𝐂𝐏 = 100%

𝑪𝒐𝒔𝒕 𝑷𝒓𝒊𝒄𝒆 = 100%

𝑳𝒐𝒔𝒔

𝑷𝒓𝒐𝒇𝒊𝒕

(𝑩𝒂𝒔𝒆 𝒗𝒂𝒍𝒖𝒆)

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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 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

% D = 30%

𝐒𝐏 = 70%

𝐌𝐏 = 100%

𝐌𝐏 = 100%


(Base value)

Discount

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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:

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%?

𝑽𝒂𝒍𝒖𝒆

𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆 𝒗𝒂𝒍𝒖𝒆× 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆 𝑽𝒂𝒍𝒖𝒆 𝒘𝒉𝒊𝒄𝒉 𝒊𝒔 𝑨𝒔𝒌𝒆𝒅

Short Trick:

Sol: = 𝑹𝒔.𝟒𝟐𝟓

𝟏𝟎𝟎%× 𝟏𝟎𝟖%

= 𝑹𝒔. 𝟒𝟓𝟗

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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: = 𝑹𝒔.𝟔𝟐𝟓𝟎

𝟏𝟎𝟎%× 𝟗𝟎%

= 𝑹𝒔. 𝟓𝟔𝟐𝟓

Short Trick: Sol: =

𝑹𝒔.𝟑𝟗𝟎𝟎

𝟏𝟐𝟎%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟑𝟐𝟓𝟎

Short Trick: Sol: = 𝑹𝒔.𝟕𝟎𝟓.𝟕𝟔

𝟖𝟖%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟖𝟎𝟐

Short Trick:

Sol: = 𝑹𝒔.𝟐𝟓𝟎

𝟏𝟐𝟓%× 𝟐𝟓%

= 𝑹𝒔. 𝟓𝟎

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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: = 𝑹𝒔.𝟑𝟕𝟓

𝟕.𝟓%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟓𝟎𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟏𝟐𝟎

𝟐%× 𝟖𝟖%

= 𝑹𝒔. 𝟓𝟐𝟖𝟎

Short Trick: Sol: = 𝑹𝒔.𝟓𝟕𝟎𝟎

𝟗𝟓%× 𝟏𝟎𝟓%

= 𝑹𝒔. 𝟔𝟑𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟏𝟗𝟓

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?

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: = 𝑹𝒔.𝟑𝟔

𝟑𝟑%−𝟐𝟕%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟔𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟏𝟔

(−𝟓)%−(−𝟕)%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟖𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟔𝟒𝟎

𝟏𝟎%−(−𝟔)%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟒𝟎𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟏𝟎𝟎

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?

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: = 𝑹𝒔.𝟏𝟎𝟓𝟎

𝟏𝟓%× 𝟖𝟓%

= 𝑹𝒔. 𝟓𝟗𝟓𝟎

Short Trick: Sol: = 𝑹𝒔.𝟔𝟓𝟑𝟔

𝟕𝟔%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟖𝟔𝟎𝟎

Short Trick: Sol: = 𝑹𝒔.𝟓𝟎𝟎

𝟐𝟓%−𝟐𝟎%× 𝟖𝟎%

= 𝑹𝒔. 𝟖𝟎𝟎𝟎

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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: 𝐍𝐞𝐭 𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭

= 𝐍𝐞𝐭 𝐄𝐟𝐟𝐞𝐜𝐭(𝟏𝟎%−, 𝟐𝟎%−, 𝟑𝟎%−)

= −𝟒𝟗. 𝟔%

Short Trick: Sol:

Rs.16000 𝟓%− 𝟏𝟔𝟎𝟎𝟎

𝟏𝟎𝟎%× 𝟗𝟓% = 𝑹𝒔. 𝟏𝟓𝟐𝟎𝟎 𝑿%

- Rs.11400

𝑿 =𝟏𝟏𝟒𝟎𝟎 − 𝟏𝟓𝟐𝟎𝟎

𝟏𝟓𝟐𝟎𝟎× 𝟏𝟎𝟎 = −𝟐𝟓 = 𝟐𝟓% 𝑫𝒊𝒔𝒄𝒐𝒖𝒏𝒕

Short Trick: Sol: 𝐍𝐞𝐭 𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭

= −𝟑𝟎 − 𝟏𝟎 +𝟑𝟎 × 𝟏𝟎

𝟏𝟎𝟎= −𝟑𝟕%

𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐃𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞

=𝐑𝐬. 𝟏𝟎𝟎𝟎

𝟏𝟎𝟎%× (𝟒𝟓 − 𝟑𝟕)%

= 𝐑𝐬. 𝟖𝟎

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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,

its equivalent “% ≡𝟏

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.

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: %𝐏 =𝐑𝐬.𝟓𝟖𝟎𝟎−(𝐑𝐬.𝟒𝟕𝟎𝟎+𝐑𝐬.𝟖𝟎𝟎)

𝐑𝐬.𝟒𝟕𝟎𝟎+𝐑𝐬.𝟖𝟎𝟎× 𝟏𝟎𝟎

= 𝟓𝟓

𝟏𝟏%

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1) The profit percentage of the shopkeeper.

2) The loss percentage of the customer.

Q.3: The cost price of an article is 𝟓 𝟕⁄𝒕𝒉

of the selling price. Find the

percentage profit or the percentage loss.

Q.4: The profit earned by selling an article is 𝟐𝟖𝟒

𝟕% of the selling price.

Find the percentage profit.

Short Trick: Sol.1: %𝐏 =

𝟏𝟎𝟎 𝐠𝐦

𝟗𝟎𝟎 𝐠𝐦× 𝟏𝟎𝟎

= 𝟏𝟏𝟏

𝟗%

Short Trick: Sol.2: %𝐏 =

𝟏𝟎𝟎 𝐠𝐦

𝟏𝟎𝟎𝟎 𝐠𝐦× 𝟏𝟎𝟎

= 𝟏𝟎%

Short Trick: Sol: 𝐂𝐏 ∶ 𝐒𝐏 = 𝟓: 𝟕

∴ %𝐏 = (𝟐

𝟓× 𝟏𝟎𝟎) %

= 𝟒𝟎%

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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: 𝟐𝟖

𝟒

𝟕% ≡

𝟐

𝟕

𝐏: 𝐒𝐏 = 𝟐: 𝟕

%𝐏 = (𝟐

𝟓× 𝟏𝟎𝟎) % = 𝟒𝟎%

Short Trick: Sol: 𝐏 ∶ 𝐒𝐏 = 𝟐𝟎 ∶ 𝟏𝟎𝟎

= 𝟏 ∶ 𝟓

%𝐏 = (𝟏

𝟒× 𝟏𝟎𝟎) % = 𝟐𝟓%

Short Trick: Sol: 𝐋 ∶ 𝐂𝐏 = 𝟏𝟎 ∶ 𝟏𝟎𝟎

= 𝟏 ∶ 𝟏𝟎

%𝐋 = (𝟏

𝟗× 𝟏𝟎𝟎) % = 𝟏𝟏

𝟏

𝟗%

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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.

𝐒𝐏 − 𝐂𝐏 = 𝐏

→ 𝟑𝟑 × 𝐒 − 𝟑𝟑 × 𝐂 = 𝟏𝟏 × 𝐒

→ 𝟐𝟐 × 𝐒 = 𝟑𝟑 × 𝐂

→ 𝐒: 𝐂 = 𝟑𝟑: 𝟐𝟐 = 𝟑: 𝟐

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

∴ %𝐏 =𝟐

𝟏× 𝟏𝟎𝟎 = 𝟐𝟎𝟎%

𝟏𝟎 × 𝐂 = 𝟗 × 𝐒

→ 𝐂𝐏: 𝐒𝐏 = 𝟗: 𝟏𝟎

∴ %𝐏 = (𝟏

𝟗× 𝟏𝟎𝟎) %

= 𝟏𝟏𝟏

𝟗%

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∴ %𝐏 = (𝟏

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

∴ %𝐏 = (𝟏

𝟑× 𝟏𝟎𝟎) % = 𝟑𝟑

𝟏

𝟑%

Short Trick: Sol: 𝐏 ∶ 𝐂𝐏 = 𝟏𝟏 ∶ (𝟑𝟑 − 𝟏𝟏)

= 𝟏𝟏 ∶ 𝟐𝟐

= 1 : 2

%𝐏 = (𝟏

𝟐× 𝟏𝟎𝟎) % = 𝟓𝟎%

Short Trick: Sol: 𝐒𝐏 ∶ 𝐂𝐏 = (𝟔𝟔 + 𝟐𝟐) ∶ 𝟔𝟔

= 𝟖𝟖 ∶ 𝟔𝟔

= 4 : 3

%𝐏 = (𝟏

𝟑× 𝟏𝟎𝟎) % = 𝟑𝟑

𝟏

𝟑%

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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 𝟐 𝟑⁄

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?

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

Sol: Let S be the original selling price.

𝟐

𝟑× 𝑺 ≡ 𝟗𝟎%

→ 𝑺 ≡ 𝟗𝟎% ×𝟑

𝟐= 𝟏𝟑𝟓%

∴ %𝑷 = 𝟏𝟑𝟓% − 𝟏𝟎𝟎% = 𝟑𝟓%


𝟒𝟎

𝟏𝟎𝟎× 𝑺 ≡ 𝟗𝟎%

→ 𝑺 ≡ 𝟗𝟎% ×𝟏𝟎𝟎

𝟒𝟎= 𝟐𝟐𝟓%

∴ %𝑷 = 𝟐𝟐𝟓% − 𝟏𝟎𝟎% = 𝟏𝟐𝟓%

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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 𝟏𝟐𝟏

𝟐% to the customer. Find his

net profit percentage in the deal.

Sol: P%


𝟔𝟎

𝟏𝟎𝟎× 𝑺 ≡ 𝟗𝟎%

→ 𝑺 ≡ 𝟗𝟎% ×𝟏𝟎𝟎

𝟔𝟎= 𝟏𝟓𝟎%

∴ %𝑷 = 𝟏𝟓𝟎% − 𝟏𝟎𝟎% = 𝟓𝟎%

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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: 𝟏𝟎%+

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: 𝟐𝟎%+ %𝐏 =?

Sol: CP 𝟐𝟓%+ MP 𝟏𝟐𝟏

𝟐%− SP

%𝑷 = 𝟐𝟓 − 𝟏𝟐𝟏

𝟐−

𝟐𝟓 × 𝟏𝟐𝟏𝟐

𝟏𝟎𝟎

∴ %𝑷 = 𝟗𝟑

𝟖%

Sol: CP 𝒙%+ MP 𝟓%− SP

𝟏𝟎 = 𝒙 − 𝟓 −𝒙 × 𝟓

𝟏𝟎𝟎

∴ 𝒙 = 𝟏𝟓𝟏𝟓

𝟏𝟗%

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Sol.2: 𝟐𝟎%+ %𝐏 =?

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 𝒙%+ MP 𝟏𝟎%− SP

𝟐𝟎 = 𝐱 − 𝟏𝟎 −𝐱 × 𝟏𝟎

𝟏𝟎𝟎

∴ 𝐱 =𝟏𝟎𝟎

𝟑%

Sol.1: CP 𝟏𝟎𝟎

𝟑%+ MP 𝟐𝟎%− SP

%𝐏 =𝟏𝟎𝟎

𝟑− 𝟐𝟎 −

𝟏𝟎𝟎𝟑 × 𝟐𝟎

𝟏𝟎𝟎

∴ %𝐏 = 𝟔𝟐

𝟑%

Sol.2: CP 𝒙%+ MP 𝟏𝟎%− SP

𝟐𝟎 = 𝐱 − 𝟏𝟎 −𝐱 × 𝟏𝟎

𝟏𝟎𝟎

∴ 𝐱 =𝟏𝟎𝟎

𝟑%

Sol.2: CP 𝟏𝟎𝟎

𝟑%+ MP 𝟎%− SP

%𝐏 =𝟏𝟎𝟎

𝟑− 𝟎 −

𝟏𝟎𝟎𝟑 × 𝟎

𝟏𝟎𝟎

∴ %𝐏 = 𝟑𝟑𝟏

𝟑%

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Sol: 𝟑𝟐%+ %𝐏 =?

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: 𝟑𝟎%+

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= 𝟒. 𝟓%+

Sol: CP 𝒙%+ MP 𝟏𝟐%− SP

𝟑𝟐 = 𝐱 − 𝟏𝟐 −𝐱×𝟏𝟐

𝟏𝟎𝟎

∴ 𝐱 = 𝟓𝟎%

Sol: CP 𝟓𝟎%+ MP 𝟐𝟎%− SP

%𝐏 = 𝟓𝟎 − 𝟐𝟎 −𝟓𝟎 × 𝟐𝟎

𝟏𝟎𝟎

∴ %𝐏 = 𝟐𝟎%

Sol: 𝐂𝐏 = 𝐑𝐬. 𝟏𝟖𝟎𝟎𝟎 𝐌𝐏 =? 𝟏𝟎%− SP

𝑴𝑷 =(

𝑹𝒔. 𝟏𝟖𝟎𝟎𝟎𝟏𝟎𝟎% × 𝟏𝟑𝟎%)

𝟗𝟎%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟐𝟔𝟎𝟎𝟎

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: 𝟏𝟎%+ ≡ 𝑹𝒔. 𝟓𝟔

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: 𝟐𝟎%+

Sol: 𝐂𝐏 =? 𝐌𝐏 = 𝐑𝐬. 𝟐𝟕𝟓𝟎 𝟓%− 𝐒𝐏

𝑪𝑷 =(

𝑹𝒔. 𝟐𝟕𝟓𝟎𝟏𝟎𝟎% × 𝟗𝟓%)

𝟏𝟎𝟒. 𝟓%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟐𝟓𝟎𝟎

Sol: 𝐂𝐏 𝐋𝐞𝐭 𝐌𝐏 = 𝟏𝟎𝟎% 𝑫, 𝟐𝟑%− 𝐒𝐏, 10% P

𝑴𝑷 =(

𝑹𝒔. 𝟓𝟔𝟏𝟎% × 𝟏𝟏𝟎%)

𝟕𝟕%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟖𝟎𝟎

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: 𝐂𝐏 =? 𝐌𝐏 = 𝐑𝐬. 𝟔𝟎 𝟏𝟓%− SP + Rs.3

𝑪𝑷 =(

𝑹𝒔. 𝟔𝟎𝟏𝟎𝟎% × 𝟗𝟓% + 𝑹𝒔. 𝟑)

𝟏𝟐𝟎%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟓𝟎

Short Trick: Sol: = 𝟑𝟎 ×

𝟏𝟎𝟎

𝟏𝟐𝟓

= 𝟐𝟒 𝐭𝐨𝐟𝐟𝐞𝐞𝐬

Short Trick: Sol: = 𝟑𝟎

𝟏𝟐×

𝟏𝟎𝟎

𝟏𝟐𝟓× 𝟏𝟑

= 𝟐𝟔 𝐭𝐨𝐟𝐟𝐞𝐞𝐬

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: = 𝟏𝟖 ×

𝟔𝟎

𝟏𝟎𝟎×

𝟏𝟎𝟎

𝟏𝟐𝟎

= 𝟗 𝐚𝐩𝐩𝐥𝐞𝐬

Short Trick: Sol: = 𝟏𝟖

𝟗𝟎×

𝟔𝟎

𝟏𝟎𝟎×

𝟏𝟎𝟎

𝟏𝟐𝟎× 𝟏𝟑𝟎

= 𝟏𝟑 𝐚𝐩𝐩𝐥𝐞𝐬

𝑪𝑷

𝑺𝑷

𝑨𝒓𝒕𝒊𝒄𝒍𝒆𝒔 𝑹𝒔.

𝒂

𝒃 𝒎

𝒏

𝑻𝒉𝒆𝒏 %𝑷 𝒐𝒓 %𝑳 = (𝒏𝒃 − 𝒎𝒂

𝒎𝒂× 𝟏𝟎𝟎) %

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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

∴𝟗 × 𝟐𝟎 − 𝟏𝟏 × 𝟏𝟔

𝟏𝟏 × 𝟏𝟔× 𝟏𝟎𝟎 = +𝟐

𝟑

𝟏𝟏% ← 𝐏𝐫𝐨𝐟𝐢𝐭

𝑪𝑷

𝑺𝑷

𝑨𝒓𝒕𝒊𝒄𝒍𝒆𝒔 𝑹𝒔.

𝟏𝟔

𝟐𝟎 𝟏𝟏

𝟗

Short Trick: Sol: = 𝟏𝟏𝟎%

𝐑𝐬.𝟓𝟎𝟔𝟎× 𝐑𝐬. 𝟒𝟑𝟕𝟎

= 𝟗𝟓% < 𝟏𝟎𝟎%(𝐂𝐏)

∴ %𝐋 = 𝟓%

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:

∴ (𝟗𝟎𝟎 − 𝐂) =𝟐𝟎𝟎

𝟏𝟎𝟎(𝐂 − 𝟒𝟓𝟎)

→ 𝑪 = 𝑹𝒔. 𝟔𝟎𝟎

Hence; 𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐒𝐏 =𝐑𝐬.𝟔𝟎𝟎

𝟏𝟎𝟎%× 𝟏𝟐𝟓% = 𝐑𝐬. 𝟕𝟓𝟎

Short Trick: Sol:

Manju +𝟏

𝟒 Anju

+𝟏

𝟏𝟎 Sonia

+𝟏

𝟐𝟎 Bobby

CP = Rs.231

𝑪𝑷 𝒇𝒐𝒓 𝑴𝒂𝒏𝒋𝒖 =𝑹𝒔.𝟐𝟑𝟏

𝟐𝟏×𝟏𝟏×𝟓× (𝟐𝟎 × 𝟏𝟎 × 𝟒)

= 𝑹𝒔. 𝟏𝟔𝟎

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: −𝟏𝟎 + 𝟐𝟓 −𝟏𝟎×𝟐𝟓

𝟏𝟎𝟎= 𝟏𝟐. 𝟓%

Q.10: The cost price of an article is 𝟐 𝟑⁄ 𝒓𝒅 of its marked price

and the marked price is 𝟒𝟑⁄ 𝒓𝒅 of the selling price. Find the

profit percentage.

Short Trick: Wholesaler Retailer 𝟏𝟎%+ Customer

Hence; 𝑪𝑷 =𝑹𝒔.𝟏𝟖

(𝟏𝟐.𝟓−𝟏𝟎)%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟕𝟐𝟎

Short Trick: Sol: 𝑪𝑷 : 𝑴𝑷 = 𝟐 : 𝟑

𝑴𝑷 : 𝑺𝑷 = 𝟒 : 𝟑

𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆; 𝑪𝑷 : 𝑴𝑷 : 𝑺𝑷 = 𝟖 : 𝟏𝟐 : 𝟗

𝑯𝒆𝒏𝒄𝒆; %𝑷 =𝟏

𝟖× 𝟏𝟎𝟎

= 𝟏𝟐. 𝟓%

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: 𝐌𝐏 ∶ 𝐂𝐏 ∶ 𝐒𝐏

= 𝟏𝟎𝟎 ∶ 𝟗𝟎 ∶ 𝟏𝟎𝟎

= 𝟏𝟎 ∶ 𝟗 ∶ 𝟏𝟎

Hence; %𝐏 = (𝟏

𝟗× 𝟏𝟎𝟎) %

= 𝟏𝟏𝟏

𝟗%

Short Trick: Sol: 𝐒𝐏(𝐒𝐡𝐨𝐩𝐤𝐞𝐞𝐩𝐞𝐫) ∶ 𝐂𝐏(𝐌𝐨𝐧𝐢𝐜𝐚) ∶ 𝐒𝐏(𝐌𝐨𝐧𝐢𝐜𝐚)

= 𝟏𝟎𝟎 ∶ 𝟗𝟎 ∶ 𝟏𝟎𝟖

= 𝟓𝟎 ∶ 𝟒𝟓 ∶ 𝟓𝟒

Hence; %𝐏(𝐌𝐨𝐧𝐢𝐜𝐚) = (𝟗

𝟒𝟓× 𝟏𝟎𝟎) %

= 𝟐𝟎%

of 33

Short Trick: Sol:

= 𝑹𝒔.𝟏𝟎

𝟏𝟎𝟎%×𝟏𝟑𝟎%−𝑹𝒔.𝟓

𝟏𝟎%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟖𝟎

myshop.mahendras.org

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: = −

𝑹𝒔.𝟐𝟎

𝟏𝟎𝟎%×𝟏𝟏𝟎%+𝑹𝒔.𝟒

−𝟏𝟓%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟏𝟐𝟎

Short Trick:

Sol: = 𝑹𝒔.𝟏𝟎𝟎

𝟏𝟎𝟎%×𝟏𝟐𝟒%−𝑹𝒔.𝟏𝟎𝟎

𝟒%× 𝟏𝟎𝟎%

= 𝑹𝒔. 𝟔𝟎𝟎

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