Profit and Loss Formula Questions

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Profit and Loss Formula

Do you aspire to study abroad? If yes, then you must be trying your best to hit the bull’s eye in the GMAT exam. Graduate Management Aptitude Test (GMAT) is a prestigious test which one has to qualify in order to opt for overseas education in the Management domain. Being one of the most reputable competitive exams, GMAT assess the applicants through sections like Logical Reasoning, Quantitative Aptitude, English Language etc. If you are appearing for the GMAT exam this year, here is a blog to help you with some profit and loss formulas and questions to practice.  

Profit and Loss Concepts

Let us check out some of the most important concepts of profit and loss. 

Profit (P)

The amount gained by selling a product with more than its cost price. 

Loss (L)

The amount that you lose after selling a product with less than its cost price. 

Cost Price (CP)

The amount paid for a product or commodity to purchase it is called a cost price. It can be divided into two parts:

  • Fixed Cost
  • Variable Cost

Selling Price(SP)

The amount for which the product is sold is called the Selling Price. 

Marked Price Formula (MPF)

Discount=Marked price- selling price
Discount percentage=(Discount/Marked price)*100

Profit and Loss Examples

  • If you buy a bag for Rs 50 and sell it for Rs 80, the profit is Rs 30.
  • If you buy a bag for Rs 50 and sell it for Rs 30, the loss is Rs 20.
  • If you buy a bag for Rs 100 and sell it for Rs 120, the profit is Rs 20%.

List of Profit and Loss Formula

Let us look at some important profit and loss formulas to get a better hold of the concept:

Gain = SP- CP 

Loss = CP- SP

Gain% = (Gain/ CP)x 100

Loss% = (Loss/ CP)x 100

SP= [(100+ Gain%)/ 100]x CP

SP= [(100- Loss%)/ 100]x CP 

CP= [100/ (100+ Gain%)]x SP

CP= [100/ (100- Loss%)]x SP

Also Read: Sequence and Series

Profit and Loss Formula Marked Price

Marked Price is an additional price that is put up by the shopkeepers upon the selling price to offer a certain discount.

Discount = Marked Price – Selling Price

Discount Percentage = (Discount/Marked price) x 100

Profit and Loss Formula with Example

Now that you are clear with profit and loss formulas, below mentioned are some solved examples that will help you understand the usage of the above-mentioned and related formulas.

Example 1: Sunita bought 10 shirts for Rs.40 and sold 8 of them at Rs. 35. Calculator gain or loss %. 

Solution:

CP of 10 toys= Rs. 40 
CP of 1 toy= Rs. 4
SP of 8 toys= Rs. 35 
SP of 1 toy= Rs. 35/8
Therefore, Gain =35/8 – 4 = ⅜
Gain percent= (3/8)/4 x 100= 9.375% 

Have a look at our blog on Sample Questions for GMAT 2021

Example 2:  A merchant sells his goods using weights 15% less than true weights and makes a profit of 20%. Find his total gain %. 

Solution:

Let us consider 1 kg of goods bag. Its actual weight is 85% of 1000gm= 850gm 
Let the cost price of each gram be Re. 1. Then the CP of each good bag= Rs. 850
SP of 1 kg bag= 120% of the true CP 

Therefore, SP 120/100 x 1000 = Rs. 1200
Gain = 1200- 850= 350
Gain %= 350/850 x 100= 41.17 %

Example 3: Riya sold a pen at a 12% profit. On selling it for Rs 18 more she would get a profit of 18%. What is the CP of the pen?

Solution:

SP = CP [1 + (Gain % x 100)]
Firstly 
SP= CP (1 + 0.12) = 1.12 CP 
Secondly
SP= CP (1 + 0.18)= 1.18 CP
So the difference between first and second cases is Rs. 18 (given)

Therefore, 
1.18 CP  – 1.12 CP = 18
0.06 CP = 18
CP = 18/0.06
CP= 300
The cost price of pen is Rs. 300

Check out: Arithmetic Questions for GMAT Quantitative Reasoning Section

Example 4: My mother bought two dresses for Rs. 2500 each. If she sells one at a profit of 5%, then at what price she should sell the other dress to make a profit of  20% on the whole.

Solution:

Let the other profit % be x  
Then, the equation becomes 
105/100 x 2500 + [(100+ x)/ 100]x 2500= 120/100 x 5000 
x= 35

Hence, if she makes a profit of 35% on the second dress, it comes to a total of 20% profit on the whole.

You cannot miss: Maths Tricks to Ace GMAT Quant Section

Profit and Loss Formula PDF

Here is a PDF that will assist you with all the important Profit and Loss formulas-

Profit and Loss Formula and Tricks for Competitive Exams

Listed below are some important tricks that can turn out to be handy during competitive exams– 

  1. For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100.
  2. When there are two successful profits say a% and b%, then the net percentage profit equals to (a+ b+ ab)/100
  3. When the profit is a% and loss is b%, then the net % profit or loss will be: (a- b -ab)/100
  4. If a product is sold at a% profit and then again sold at b% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100+a)(100+b)]. In case of loss, CP = [100 x 100 x P/(100-a)(100-b)]
  5. If P% and L% are equal then, P = L and %loss = P2/100
  6. Profit, P = SP – CP; SP>CP
  7. Loss, L = CP – SP; CP>SP
  8. P% = (P/CP) x 100
  9. L% = (L/CP) x 100
  10. SP = {(100 + P%)/100} x CP
  11. SP = {(100 – L%)/100} x CP
  12. CP = {100/(100 + P%)} x SP
  13. CP = {100/(100 – L%)} x SP
  14. Discount = MP – SP
  15. SP = MP -Discount

Profit and Loss Formula for Bank Exam

Apart from the above-mentioned formulas, here are the ones that can help you in qualifying bank exams-

  1. Profit% Formula= 100 x Profit/Cost Price
  2. Loss Percentage Formula= 100 x Loss/Cost Price
  3. Profit= Selling Price – Cost Price (when SP>CP)
  4. Loss= Cost Price – Selling Price(when CP>SP)
  5. Discount= Marked Price – Selling Price
  6. Selling Price= Marked Price – Discount

Profit & Loss: Solved Examples, Practise Time!

An article is sold for Rs 2400 at a profit of 25 %. What would have been the actual profit or loss if it had been sold at Rs 1800?

Firstly let us find the cost price of the same. C.P. = 2400 × 100/125 = 1920.
New selling price = Rs. 1800 ⇒ Loss = 1920 – 1800 = 120
∴ Loss percentage = 100 × 120/1920 = 6.25%.

If an article is sold at a loss of 66 2/3%, what is the loss in terms of the selling price?

Let the C. P. = 100. ∴ Amount of loss = 66 2/3 or 200/3 ⇒ S. P = 100 – 66 2/3 = 33 1/3 or 100/3.
∴ Loss expressed in terms of S. P. = 100 × (200/3)/(100/3) 100 = 200 %

A man sells two chairs for Rs. 480 each. On one he makes a profit of 20 % and on the other he makes a loss of 20 %. Find his total loss/gain in these two transactions (in Rs.).

Here the amount of loss can be directly found by the formula given in the formula section of this article.
The amount of loss = 2.p2.S.P/1002-p2 ∴ ⇒ Loss = 2.202.480/1002-202 = 40. So net loss = Rs. 40.

A package tour operator allows a 25 % discount on his advertised price and then makes a profit of 20 %. What is the advertised price on which he gains Rs. 60?

Profit = Selling price – Cost Price = 60. Selling price = 1.2 (C. P.) ⇒ 1.2 C.P – C. P. = 60.
⇒ 0.2 C. P. = 60 ⇒ C. P. = 300 and Selling price = 360.
List price or advertised price ⇒ (0.75) = Selling price ⇒ List price = Selling price/0.75 = 360/0.75 = Rs. 480.

A man sold Pentium computers at a profit of 6 %. Had he made a loss of 5 % instead due to a price crash, he would have sold it for Rs 3,850 less. What was his cost price and selling price in each of the instances?

C. P. (1.06) = S.P.1
C. P. (0.95) = S.P.2
S. P.1 – S. P.2 = 3850 ⇒ C. P. (1.06 – 0.95) = 3850 ⇒ 0.11 C. P. = 3850 ⇒ C. P. = 35,000.
And S. P.1 = 1.06 × 35,000 = 37,100 and S. P.2 = 0.95 × 35,000 = 33,250

Henry sold a bicycle at 8% gain. Had it been sold for $ 75 more, the gain would have been 14%. Find the cost price of the bicycle.

Let the cost price of the bicycle be $ x.
SP of the bicycle at 8% gain = $ [{(100 + gain %) /100} × CP]= $ [{(100 + 8)/100} × x] = $ {(108/100) × x} = $ (27x/25)

An article is bought for Rs. 675 and sold for Rs. 900. Find the gain percent?

900 – 675 = 225
225/675*100
= 33 1/3%

A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?

Total C.P. = 45
Total S.P. = 60
Profit% = (15/45) *100 = 33.33%

A trader sells 85 m of cloth for Rs. 8,925 at the profit of Rs. 15/m of cloth. What is the cost price of 1 m of cloth?

SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth – profit on 1m of cloth
= Rs. 105 – Rs. 15 = Rs. 90

Amit bought 160 shirts at the rate of Rs. 225/shirt. The transport expenditure was Rs. 1,400. He paid an octroi at the rate of Rs. 1.75/shirt and labour charges were Rs. 320. What should be the selling price of 1 shirt, if he wants a profit of 20%?

Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]= 237.5 * [(100 + 20)/100] = Rs. 285

Profit after selling a commodity for Rs. 425 is same as loss after selling it for Rs.355. The cost of the commodity is?

Let C.P = Rs. X
425 – X = X – 355 (or)
2X = 780 or X = 390

Bhajan Singh purchased 120 reams of paper at Rs. 80 per ream. He spent Rs. 280 on transportation. Paid octroi at the rate of 40 paise per ream and paid Rs. 72 to the coolie. If he wants to have a gain of 8 %. What must be the selling price per ream?

C.P of 120 reams = Rs. (120 × 80 + 280 + 72 + 120 × 40) = Rs. 10000
C.P of 1 ream = (10000/120) = Rs. (250/3)
S.P of 1 ream = Rs. (108/100 × 250/3) = Rs. 90

More Practice Questions

After these examples, now let us check how much you have grasped the profit and loss formulas by solving the below-mentioned questions on your own.

  1. In a certain mart, the profit is 320% of the total cost. If the cost increases by 25% but the SP remains constant, approximately what percentage of the selling price is profit?
  2. If the selling price is doubled, the profit triples. Find the profit per cent 
  3. Himanshu bought 6 pencils for a rupee. How many for a rupee he must sell to gain 20% profit?
  4. A manufacturer sells a table for Rs. 2400 and made a profit of 25% in the process. Find his total profit percent if he had sold his good for Rs. 2040.
  5. While selling 10 mangoes, a fruitseller incurred loss equal to the cost price of 3 mangoes. Find the loss percent. 
  6. An article is sold for Rs 5400 at a profit of 35 %. What would have been the actual profit or loss if it had been sold at Rs 2800?
  7. Aman, Bharat and Chhavi enter into a partnership. Aman invests some money at the beginning, Bharat invests double the amount after 6 months, and Chhavi invests thrice the amount after 8 months. If the annual gain is Rs. 18,000. Aman’s share is?
  8. Profit obtained by selling a dress at Rs. 520 is equal to 7/5th of the profit obtained by selling the same dress at Rs. 800. What is the cost price of the dress?
  9. A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?
  10. Harpreet Singh purchased 120 reams of paper at Rs. 80 per ream. He spent Rs. 280 on transportation. Paid octroi at the rate of 40 paise per ream and paid Rs. 72 to the coolie. If he wants to have a gain of 8 %. What must be the selling price per ream?
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Thus, we hope that this blog on profit and loss formulas helped you gain insight into the concept. Do you aspire to study abroad but are clueless about how to proceed? Reach out to Leverage Edu and we will help you get started on the right career path.

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