One of a crucial chapter in arithmetic part of Quantitative Aptitude section in any competitive exam. The question related to this topic can be straight or might be clubbed with other topics like data interpretation. In order to help candidates, to prepare this topic in a better way here we discuss about the topic and try to cover all the concepts.

**Let’s take an example:**

Avinash was travelling from Bangalore to Hyderabad by Bus. At bus stop, Avinash purchased a book “3 Mistakes”. The price printed on the book was 500. After negotiation with vendor he asked to give him 30% discount. Vendor denied first but finally agreed for a discount of 20%. He read the book in Bus when he reached Hyderabad, Avinash sold the book to Rakshit for MRP marked on the book. After reading the book, Rakshit also sold the book to Ranjit after giving discount at Rs.400.

**Now, let’s look at most common questions.**

**What is the MRP of Book?**

MRP: the price printed on an object is called Marked Retail Price. Therefore MRP of the Book is 500.**What is the discount?**

Discount should always be calculated over MRP, Avinash and vendor both finally agreed at discount of 20%.

Discount = 20% of MRP = 20% of 500

= (20×500)/100 = 100**What’s the Selling Price of Book for Vendor?**

Selling Price (SP) is the price at which an object is sold.

SP = MRP – discount

SP = 500 – 100= Rs.400**What’s the Cost Price of Book for Avinash?**

Cost Price is the price at which an object is purchased.

Avinash purchased this Book at Rs.400.**What’s the Selling Price of Book for Avinash?**

Avinash sold the book at the MRP, therefore the SP for Avinash is 500.**What’s the Cost Price of Book for Rakshit?**

Rakshit purchased the book at MRP. therefore CP for Rakshit is Rs.500.**How much profit did Avinash?**

Avinash purchased it at Rs.400 and sold it at Rs. 500

So, Profit = SP – CP = 500 -400 = Rs.100**What’s the SP for Rakshit?**

He sold it to Ranjit at Rs. 400. therefore SP for Rakshit is Rs.400**What discount did Rakshit give to Ranjit?**

Discount = CP of Rakshit – SP of Rakshit

= 500 – 400 = 100**How much discount% was given to Ranjit by Rakshit?**

discount% = (Discount/ CP for Rakshit)× 100

= (100/500)× 100

= 20%**How much Loss did Rakshit inccur?**

Loss = CP for Rakshit – SP for Rakshit

Loss = 500 – 400 = 100 Rs.

Let’s discuss a few more example:

**Example 1:**

If a shopkeeper purchases 12 balls for Rs.10 and sells 10 balls for Rs.12. What was his profit or loss he made?

**Approach:**

We can observe that the shopkeeper purchased more balls at a lower price and then sold less balls at a higher price. So, definitely we confidently conclude that the shopkeeper made profit. Therefore we can easily eliminate the options which reflects loss.

**Solution: **

CP of 12 balls = Rs.10

SP of 10 balls =Rs. 12

So, SP of 12 balls = (12/10)× 12 = 14.4

Profit% = ((SP-CP)/CP)× 100 = (4.4/10)× 100= 44%

**Tricks for this type of questions:**

Purchases : 12 balls for Rs.10

Sells : 10 balls for Rs.12

For profit% or loss% Cross multiply

profit% or loss% = ((12× 12 – 10× 10)/(10× 10))× 100

= 44%

**Example 2:**

If a shopkeeper purchases 12 balls for Rs.10 and sells 10 balls for Rs.8. What is the profit or loss he beared?

**Solution:**

There is clear loss by using approach above.

profit% or Loss% = ((12×8-10×10)/(10× 10))× 100

= -4% (negative sign represents loss)

Therefore loss is 4%.

SP = [(100±profit or loss)/100]× CP

**Example 3:**

A man sold a tv for ₹890 having 11% loss. What should be the price of tv if it is sold at 10% profit?

**Solution:**

SP_{1}= 890 , loss 11%

We know that loss% = [(CP-SP)/CP]×100

11CP =(CP-890)×100

11CP = 100CP – 890×100

89CP = 890×100

CP = 1000

If the tv was sold at 10% profit,

then new SP = CP + 10%CP

New SP = 1000+100 = 1100

**Approach:**

Loss is 11% and is always calculated on CP, So the loss is = 11% CP

New SP = [(100±new profit or loss %)/100]× CP….(1)

Old SP = [(100±old profit or loss%)/100]×CP….(2)

CP = Old SP/ [(100±old profit or loss%)/100]….(3)

Now, placing eqn 3 in eqn 1.

New SP = Old SP [(100±new profit or loss %)/(100±new profit or loss %)]

New SP = 890 [(100+10)/(100-11)] = 1100

**Example 4:**

A man sold an phone for Rs.6080 after 20% discount on the marked price. he makes 18% profit on cost price. What is the profit percentage if no discount was given?

**Solution:**

SP = MP (100-discount)%

6080 = MP (80%)

MP = 7600

Also, SP = CP [(100+profit%)/100]

SP = CP(118/100)

CP = (6080×100)/118

CP = 5125.54

He sold it at MP.

Therefore the New SP = MP

profit% = [(MP-CP)/CP]×100

= [(7600-5125.24)/5125.24]×100

=47.5%

**Another approach:**

Reqd. profit% = [(Discount±Profit or loss)/(100-discount%)]× 100

Reqd. profit% = [(20+18)/(100-20)]× 100

Reqd.profit% = 380/8 = 47.5%

**Example5:**

A man sold a project at 25% profit after giving 20% discount. Find the ratio between:

Cost price, selling price and Marked price.

**Solution:**

Let Cost price be Rs.100.

SP = (125/100)×100 = 125

SP = [(100-discount%)/100]MP

SP = (80/100)MP

MP= (125×100)/80

MP= 625/4

ratio CP : SP :MP

100 : 125 : (625/4)

4 : 5 : (25/4)

16: 20 :25

**Another approach:**

Let MP is 100 Rs

MP = 100

SP = 80

then, SP =125% of CP

So, CP = 64

ratio of CP:SP:MP

= 64:80:100

= 16:20:25

Dishonest man Concept

These are a few basic examples that covers almost all topics and concepts under profit, loss & discount. Hope that you get benefited with this discussion and may you do well in all your exams, Good Luck!

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