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Aptitude Partnership Theory

Formulas

Simple Partnership:

$\dfrac{Capital\:of \:A}{Capital \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$

Capital of A : Capital of B = Profit of A : Profit of B

Compound Partnership:

$\dfrac{Capital\:of \:A\times Time\: Period \:of \:A}{Capital \:of \:B\times Time \:Period \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$

Capital of A × Time period of A : Capital of B × Time period of B = Profit of A : Profit of B

If n partners are investing for different period of time then

C1T1 : C2T2 : C3T3 : … : CnTn = P1 : P2 : P3 : … : Pn

Where C is the capital invested, T is time period of capital invested and P is profit earned.

Partnership:

When more than one person agree to invest their money to run a business or firm then this kind of agreement is called partnership. The persons involved in the partnership are called partners.

Two types of partnership.

  • Simple Partnership
  • Compound Partnership

Simple Partnership:

If two partners A and B are investing their money to run a business,capitals of partners are invested for the same period of time.

$\dfrac{Capital\:of \:A}{Capital \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$

Capital of A : Capital of B = Profit of A : Profit of B

  • Example:

    P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, then find the amount invested by Q?

    Let the amount invested by Q = q

    40000:Q=2:3

    40000×3=2Q

    $Q=\dfrac{40000\times3}{2}$

    Q=60000

  • Exercise:

    44222.A and B starts a business investing Rs.85000 and Rs.15000 respectively. Find out the ratio in which the profits should be shared.
    10 : 3
    17 : 3
    3:5
    3 : 17
    Explanation:

    Here A's and B's capitals are there for equal time. Hence

    A : B = 85000 : 15000

    = 85 : 15

    = 17 : 3

    Compound Partnership:

    If two partners A and B are investing their money for different period of time to run a business, capitals of partners are invested for the different period of time.

    $\dfrac{Capital\:of \:A\times Time\: Period \:of \:A}{Capital \:of \:B\times Time \:Period \:of \:B}=\dfrac{Profit\:of \:A}{Profit\: of \:B}$

    Capital of A × Time period of A : Capital of B × Time period of B = Profit of A : Profit of B

  • Example:

    Jack and Jill start a business by investing 2,000 for 8 months and 3,000 for 6 months respectively. If their total profit is 510 and then what is profit of Jill?

    Capital of Jack = 2000 and Time period = 8 months

    Capital of Jill = 3000 and Time period = 6 months

    $\dfrac{Capital\:of \:Jack\times Time\: Period \:of \:Jack}{Capital \:of \:Jill\times Time \:Period \:of \:Jill}=\dfrac{Profit\:of \:Jack}{Profit\: of \:Jill}$

    $\dfrac{2000\times 8}{3000\times 6 }=\dfrac{Profit\:of \:Jack}{Profit\: of \:Jill}$

    So, Profit of Jack : Profit of Jill = 8 : 9

    So we have 8 + 9 = 17 parts of total profit.

    Out of this 17 parts, Jack will get 8 parts and Jill will get 9 parts.

    Now, total profit is 510

    So, One Part = 510/17 = 30.

    Jill’s profit = 30 × 9 = 270 and

    Jack’s profit = 30 × 8 = 240.

  • Exercise:

    44223.A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
    5 months
    6 months
    7 months
    8 months
    Explanation:

    Let B joined for X months. Then

    85000×12:42500×X=3:1

    850×12:425X=3:1

    850×12×1=3×425X

    850×4=425X

    X=8

    If n partners are investing for different period of time then

    C1T1 : C2T2 : C3T3 : … : CnTn = P1 : P2 : P3 : … : Pn

    Where C is the capital invested, T is time period of capital invested and P is profit earned.

  • Example:

    Raju, Kamal and Vinod start a business by investing Rs 5,000 for 12 months, Rs 8,000 for 9 months and Rs 10,000 for 6 months. If at the end of the year their total profit is Rs 2000 then find the profit of each partner?

    Raju’s investment is 5000 for 12 months.

    Kamal’s investment is 8000 for 9 months.

    Vinod’s investment is 10000 for 6 months.

    So their ratio of investments is

    5000 × 12 : 8000 × 9 : 10000 × 6

    60 : 72 : 60

    5 : 6 : 5

    So their profit,

    Raju : Kamal : Vinod = 5 : 6 : 5

    So there are 5 + 6 + 5 = 16 parts of profit.

    Out of these 16 parts, Raju will get 5 parts, Kamal will get 6 parts and Vinod will get 5 parts.

    So, Total profit = 2000

    Raju’s profit =$\dfrac{5}{16} \times 2000$ = 625

    Kamal’s profit = $\dfrac{6}{16} \times 2000$ = 750

    Vinod’s profit = $\dfrac{5}{16} \times 2000$ = 625

  • Exercise:

    44224.A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
    Rs.3750
    Rs.3000
    Rs.3050
    Rs.3700
    Explanation:

    =6000*5:3600*6:7500*3

    =60*5 : 36*6 : 75*3

    =100: 72: 75

    So there are 100 + 72 + 75 = 247 parts of profit.

    Out of these 247 parts, A will get 100 parts, B will get 72 parts and C will get 75 parts.

    Total profit = 7410

    Share of A=$\dfrac{100}{247}\times 7410 $= 3000

    Two types of partners

    • Sleeping Partner
    • Working Partner

    Sleeping Partner:

    Sleeping partner is the person who provides only investment but does not take part in running the business.

    Working Partner:

    Working partner is the person who not only invests the money but also takes part in running the business. For this work he is paid some salary or some percent of profit in addition.

  • Example:

    Raju and Ramu enter into partnership,investing Rs.3000 and Rs.2000 respectively.Raju was the sleeping partner.At the end of the month,both got Rs.150 each.What was Ramu's remuneration for his work?

    Raju,Ramu's investments 3000,2000

    Profit Ratio=3:2

    Raju 3 parts=Rs.150

    Ramu has to be get 2 parts=Rs.100

    So Ramu get additional (150-100)=Rs.50 as remuneration.

  • Exercise:

    44225.A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
    Rs.4200
    Rs.3200
    Rs.2200
    Rs.5200
    Explanation:

    A's investment:B's investment

    15000:25000

    15:25

    3:5

    So there are 3+5 = 8 parts of profit.

    Total Profit=9600

    A receives 10% of the profit

    9600*10/100 = 960

    Total Profit-A's 10% profit

    9600 - 960 = 8640

    So,

    A's Share

    =8640*3/8

    = 3240

    Therefore Total Amout Received by A is

    = 3240 + 960

    = 4200

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