UGC NET Study Notes on Profit, Loss & Discount

By Mohit Choudhary|Updated : August 8th, 2022

Profit, Loss and Discount is a crucial topic in the Maths section of the UGC NET Paper 1 Exam. You may also find the application of this topic in certain Data Interpretation questions. To help you all prepare for this topic better, we will discuss this topic today.

Tips and Tricks for Profit, Loss and Discount

Let us now discuss this topic. Consider the information below:

1. Raunak was travelling to Jaipur from New Delhi by train. At the platform, he purchased the novel “Half Girlfriend”. The printed price of the novel was 250. He negotiated with the vendor and asked for a discount of 30%. The vendor didn’t agree with 30% and finally deal ended at 20% discount. He studied the novel in train and after reaching Jaipur, Raunak sold it to Manish at the MRP of the novel. After studying the novel Manish sold it to Navneet after giving some discount with the final price at Rs. 150.

Now, let us have a look at some common questions or terms that often confuse students. 

a. What is the MRP of the novel?
MRP: Marked Retail Price is the price which is printed on an object. So, the MRP of the novel is 250.

b. What is the discount?
Discount is calculated on MRP, Raunak and vendor both agreed at a 20% discount.
So, Discount = 20% of MRP = 20% of 250 = (20×250)/100 = 50.

c. What is the Selling Price of the novel for the Vendor?
Selling Price (SP) is the price at which an object is sold.
SP = MRP – discount
SP = 250 – 50 = Rs. 200.

d. What is the Cost Price of the novel for Raunak?
Cost Price is the price at which an object is purchased. Raunak purchased this novel at Rs. 200.

e. What is the Selling Price of the novel for Raunak?
Raunak sold it at the MRP, so the SP for Raunak is Rs. 250.

f. What is the Cost Price of the novel for Manish?
Manish purchased it at the MRP. So, CP for Manish is Rs.250.

g. What is the profit for Raunak?
Raunak purchased it at Rs.200 and sold it at Rs. 250
So, Profit = SP – CP = 250 -200 = Rs. 50

h. What is the SP for Manish?
He sold it to Navneet at Rs. 150. So, SP for Manish is Rs.150.

i. How much discount Manish give to Navneet?
Discount = CP of Manish – SP of Manish
 = 250 – 150 = 100

j. What is the discount % given to Navneet by Manish?
discount% = (Discount/ CP for Manish)× 100
= (100/250)× 100
= 40%

k. What is the Loss for Manish?
Loss = CP for Manish – SP for Manish
Loss = 250 – 150 = Rs. 100 

Now, we will discuss concepts by solving the questions based on this topic.

Example 1: If a man purchases 12 toys for Rs. 10 and sells 10 toys for Rs. 12. How much profit or loss does he make?

You can see that the man purchases a number of toys at less price than selling less number of toys at more price. So, definitely, we can say that he makes the profit. In the exam the options which have the loss, you can easily eliminate those options.


CP of 12 toys = Rs. 10
SP of 10 toys = Rs. 12
So, SP of 12 toys = (12/10)× 12 = 14.4
Profit% = ((SP-CP)/CP)× 100 = (4.4/10) × 100%
Tricks for this type of questions:
Purchases:    12 toys for Rs.10
Sells:            10 toys for Rs.12
For profit% or loss% Cross multiply
profit% or loss% = ((12× 12 – 10× 10)/(10× 10))× 100 = 44%


Example 2: A person sells an article for ₹890 at a loss of 11%. What will be the price of the article when sold at a profit of 10%?

SP1 = 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 he had sold it at 10% profit,
then new SP = CP + 10%CP
New SP = 1000+100 = 1100
Approach: Loss is 11% and it is calculated on CP, So we can say loss = 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, putting eqn 3 it in eqn 1.
New SP = Old SP [(100±new profit or loss %)/(100±new profit or loss %)]
Important: Put + sign for-profit and – sign for negative.

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

Example 3: A shopkeeper sold an item for Rs.6080 after giving 20% discount on the labelled price and made 18% profit on the cost price. What would have been the percentage profit if he had not given the discount?

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. So New SP = MP
profit% = [(MP-CP)/CP]×100
= [(7600-5125.24)/5125.24]×100
Another approach:
Reqd. profit% = [(Discount±Profit or loss)/(100-discount%)]× 100
Reqd. profit% = [(20+18)/(100-20)]× 100
Reqd.profit% = 380/8 = 47.5%

Example 4: A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 900gm of weight for the kg. Find his gain percent.

Solution: Let the price of 1kg is Rs.100 then, the price for 900gm will be Rs.90.
Hence, he sells 900gm instead of 1kg for Rs.100 but cost price of it is only Rs.90.
So he earns a profit of Rs.10 on Rs.90 not on Rs.100 
So, profit% = (10/90)×100
 = 11(1/9)%
You can also use formula:
gain% = [Error/(true value-error)]×100
gain% = [100/(1000-100)]×100
  = 100/9 = 11(1/9)%


Example 5: A machine is sold for Rs.5060 at a gain of 10%. What would have been the gain or loss if it had been sold for Rs.4370?

SP = CP × [(100+10)/100]
SP = CP×(11/10)
CP = 4600
New SP = 4370
Loss% =(230/4600)×100 = 5%

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All the Best for Exams,
Team BYJU'S Exam Prep


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