This topic is a pure application of Unitary method. Every trader does business in order to make profits.

The cost at which he buys goods is known as ‘Cost Price’. If he is making a product with raw materials  purchased, all the cost incurred in making the final product is ‘cost Price’ (C.P).

The price at which he sells the product is known as ‘Selling Price’ (S.P).

In transactions where

    S.P > C.P , he  makes ‘profit’

Transactions where

   C.P > S.P, he makes ‘loss’.

☛ Profit = S.P – C.P

☛ Loss = C.P – S.P

Eg. A trader buys cups from a manufacturer at Rs. 100 and sold it for Rs. 120 to his customer. Did he gain or lose in this transaction?

Here, CP = Rs.100

S.P = Rs. 120

S.P > C.P. Therefore the trader has made a profit.

Profit = Rs. 120 – Rs.100

            = Rs. 20

☛ Profit % and Loss % are always calculated by taking C.P as the base.

Profit % = Profit /C.P x 100

Loss % = Loss/C.P x 100

In the previous example, the profit was Rs. 20 on a base (investment) of Rs.100.

Profit % = 20/100x 100 = 20%

Depending on outcome of the transaction,

S.P = C.P + Profit   or

S.P = C.P – Loss

Eg. A vegetable seller bought vegetables for Rs. 1800 from the market. After selling all the vegetables, he was left with Rs. 700 profit. Calculate the S.P


C.P = Rs. 1800. 

Profit = Rs. 700

S.P = Profit + C.P

= Rs. 1800+ Rs.700

=Rs. 2500

Finding S.P with Profit/ Loss % and C.P

Many a times, we may have only Profit % and Cost Price, with which we may have to find the Selling Price.

Eg. Let us say, a man makes profit of 5% on C.P of Rs. 1200. What is the selling price? 


 As we know, profit is always calculated with CP as the base.

If the profit is 5%, it means that, for a C.P of every Rs. 100, he makes Rs. 5 profit.

Thus for every Rs. 100 as C.P,  Rs. 105 is S.P

When C.P is Rs. 1200, What will be S.P? – Application of Unitary method

Hence, S.P = 1200/100*105

= Rs. 1260

Eg. Let us say a man made a loss of 20% on articles bought for Rs. 1500. What would the selling price?


Applying a similar approach as above, for a C.P of Rs. 100, man made a loss of Rs. 20.

S.P = Rs. 80 when C.P= Rs. 100

When C.P = Rs.1500,

S.P = 80/100 X 1500

      = Rs.1200


Discount Problems

When we go to a shop, discount is one thing everyone keeps looking for.

It is nothing but the difference between the price originally quoted by shopkeeper (Marked Price) and the final price you buy it for (Selling Price).

 ☛ Discount

     = Marked Price – Selling price

Discount is always applied considering Marked Price as the base.


    =Discount/Marked Price x 100

Eg. If a product’s Marked Price is Rs.200 and 30% is the discount given, then the object is sold for Rs.30 discount.
Discount = 30 / 200 x 100
Hence, Discount = Rs. 60

Thus, Product was sold for Rs.140

Eg. A shopkeeper gave a discount of 10% but still managed to make a profit of 20% over Cost Price of Rs. 3000. What was the marked price of the product?


The cost price of product is Rs. 3000.

Profit % = 20%

Profit = 20/100 x 3000 = Rs. 600

S.P = Rs. 3000+ Rs.600

= Rs.3600

Discount % = 10 %

It means that if the marked price is Rs. 100, the discount is Rs. 10 and the Selling price is Rs. 90.

Here SP = Rs.3600, therefore,

C.P = 3600/90 x 100

= Rs. 4000.



People invest in business to make profits. When two or more people invest in a business, it is known as ‘Partnership’.

Whenever a profit is made by a business, amount invested and duration for which the amount was invested dictates the ratio in which profit is shared by the partners.


Profit ( directly proportional ) Investment

Profit (directly proportional) Time for which investment is done.



 P1 – Profit by 1st Person

I1 – Investment by 1st person

T1– Time for which money was invested by 1st person

P2 – Profit by 2nd Person

I2 – Investment by 2nd person

T2 Time for which money was invested by 1st person

Eg. A and B entered into a partnership where A invested Ra.300 for first 3 months and Rs. 600 for next 9 months. On the other hand, B invested Rs.500 for the entire year. In what ratio will their profit of Rs. 820 be divided?



= ((300×3)+(60×9))/(500×12)

 = 6300/6000

 = 21/20

If the profit was Rs.41, A would receive Rs. 21 and B would receive Rs.20.

When profit is Rs.820, A will receive 820/41 x 21 = Rs. 420 and B will receive Rs. 400.


Created on By venkateshj

Profit , Loss & Partnership - Concept Refresher

1 / 39

A, B and C enter into a partnership in the ratio  4:2:3. After 4 months, A increases his share by 40%. If the total profit at the end of 14 months be Rs.71000, then B's share in the profit is:

2 / 39

 A,B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 65000 for 6 months, B, Rs. 84000 for 2.5 months and C, Rs. 10,000 for 15 months. The profit earned was Rs. 45000. Calculate the share of A in the profit.

3 / 39

Suresh buys an article and sells it a profit. He notices that had the selling price been doubled, the profit would have been four time the current profit. Find his original profit percent.

4 / 39

Krish gets a discount of  20% on purchasing 100  tea cups from Vijay. He sells them and makes a profit equal to the undiscounted price of 20 teacups. What is the gain percentage of Krish?

5 / 39

The cost price of 30 articles is equal to the selling price of  Y articles. If the profit is 20%, find the value of Y.

6 / 39

Venu buys a old furniture for Rs. 8500 and spends Rs.3500 on its repairs. H finally manages to sell it to his at Rs.13500. What is his profit percentage in the transaction?

7 / 39

A shopkeeper always weighs 20% less than the correct weight.  Had the weight been correct, he would have gained 20% profit, what is the effective percentage of profit in this type of  transaction?

8 / 39

Gokul marked a laptop 30% over its cost price and then gave a discount of 15% . What is his profit percentage?

9 / 39

Two successive discounts of 40% and 5% are equivalent to a single discount of

10 / 39

The cost price of a mobile phone is 70% of its selling price. Find the profit percentage.

11 / 39

Amrish sold his goods after announcing two successive discounts of 30% and 20%. Find his effective discount percentage

12 / 39

Rahul gave a discount of 20% on the marked price of his and then sold it. He made a profit of 20%. By what percentage did he mark the watch above its cost price?

13 / 39

A trader marked his goods 30% above his cost price. He then gave a discount of 20%. Find his profit percentage.

14 / 39

If Kevin sold an article at three-fourth of its actual selling price, he would have incurred a loss of 25%. Find his actual profit / loss percentage.

15 / 39

Sriram bought two laptops at same price. However, he sold one at a profit of 40% and other at a loss of 40%. Find his overall profit / loss in the transaction.

16 / 39

Soham bought some chocolates at a rate of 20 chocolates for Rs.25 and the same number of chocolates at a rate of 18 chocolates for Rs. 45. He sold all of them at a rate of Rs. 2 per chocolate. Find his profit/loss in the transaction.

17 / 39

Ashish purchased tables and chairs for Rs.21000. He sold chairs worth one-third of the  cost price,  at 20% loss. Find the profit percentage at which the rest of the goods must be sold to realize an overall profit of 20%.

18 / 39

Gopal bought 15 kg of tea powder for Rs.510. He was forced to sell them at a loss equal to the amount he would have realized by selling 2 kg. Find his selling price per kg.

19 / 39

Swati sold a table at 20% loss. If he sold it at 5% profit, he would have earned Rs.900 more. Find the cost price the table.

20 / 39

A sold a chair to B at 10% loss. B sold it to C at 30% profit. If C bought it for Rs.5850, find the price at which A bought the chair.

21 / 39

A trader promised his customers to sell at cost price. But he cheats his customers by giving 200 gms less for every 1.5 kg that he sells. Find his profit percentage.

22 / 39

The profit made by selling 200 m of a cloth equals the selling price of 25 m of that cloth. Find the profit percentage made.

23 / 39

The cost of 10 cups equals the selling price of 9 cups. Find the profit/loss percentage in the complete transaction

24 / 39

Suresh calculated his  loss percentage on his selling prices. Find his actual loss percentage if he calculated loss percentage as 20%

25 / 39

Suresh calculated his profit percentage on his selling prices. Find his actual profit percentage if he calculated  his profit percentage to be 30%

26 / 39

Sharat gained 20% by selling a teapot at Rs.180. Find his gain percentage if he sells it for Rs.200.

27 / 39

Ganesh bought a gift article for Rs.1250 and sold it for Rs.1400. Find his profit percentage.

28 / 39

Jubin started a business investing Rs. 80,000. Shriya joined him after three months with an amount of Rs.1,00,000 and Shikhar joined them with Rs. 1.2 lakhs after another three months. The amount of profit earned should be distributed in what ratio among Jubin, Shriya and Shikhar respectively, 3 years after Jubin started the business?

29 / 39

A began a business with Rs. 45,000. He was joined afterwards by B with Rs. 90,000. After how many months does B join, if the profits at the end of two years  are divided in the ratio of 2:3?

30 / 39

A and B started a business in partnership investing Rs. 80,000 and Rs. 90,000 respectively. After twelve months, C joined them with Rs. 1,20,000. What will be B's share in total profit of Rs.4.6 lakh earned at the end of 2 years from the starting of the business

31 / 39

Ram, Sham, Dham rent a pasture. Ram puts 12 oxen for 7 months, Sham puts 18 oxen for 4 months and Dham puts 12 oxen for 4 months for grazing. If the rent of the pasture is Rs. 8500, how much must Ram pay as his share of rent?

32 / 39

A and B started a partnership business investing some amount in the ratio of 2 : 3. C joined then after four months with an amount twice that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

33 / 39

A and B entered into partnership with capitals in the ratio 9 : 10. After 3 months, A withdrew  1/3 rd  of his capital and B withdrew  1/5th  of his capital. The gain at the end of 1 year was Rs.30,500. How much money did A receive at the end of year?

34 / 39

Ganesh starts business with Rs. 45000 and after 3 months, Gopi joins with Ganesh as his partner. After a year, the profit is divided in the ratio 3:4. How much capital did Gopi contribute?

35 / 39

Three partners shared the profit in a business in the ratio 4: 3 : 7. They had partnered for 14 months, 7 months and 6 months respectively. What was the ratio of their investments?

36 / 39

A, B and C together invest Rs. 1,20,000 in a business for the same duration. A invests Rs. 16,000 more than B and B invests Rs. 4000 more than C. Out of a total profit of Rs. 84,000 how much does B receive?

37 / 39

Shriman started a software business by investing Rs. 1,30,000. After 10 months, Surya joined him with a capital of Rs. 180,000. After 3 years, they earned a profit of Rs. 90,300. What was Shriman's share in the profit?

38 / 39

Arjun, Kamal and Gopal invested Rs. 5000, Rs. 4000 and Rs. 6000 respectively in a business. Arjun left after 8 months. If after 12 months, there was a gain of Rs. 40000, then what will be the share of Arjun?

39 / 39

A, B and C jointly  started a business venture. A would invest Rs.15000 for 12 months, B would invest Rs.25000 for 11 months and C would invest Rs.19500 for 10 months. A was the only working person and hence receives 10% of the profits as his salary. The profit earned was Rs.65000. Calculate the total money received by A

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