# How to solve Partnership Problems ? - Concept and Problems

Dear Readers, Today we will discuss on Partnership topic of Quantitative section.Now a days this topic have became an important part of the Quantitative test in various competitive exams.
When two or more than two persons run a business jointly,they are called ‘partners’. In the business the deal between them is known as ‘Partnership’.

## Types of Partnership:

1. Simple Partnership: When investments of all the partners are for the same period of time, the profit & loss is distributed among the partners in the ratio of their original investments.
2. Compound Partnership: When investments of all the partners are for different period of time. then equivalent capitals are calculated for a unit of time and profit or loss is divided in the ratio of the product of time and investment.

## Ratio of Divisions of Gains:

1. When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

(A’s share of profit) : (B’s share of profit) = x : y.

2.When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,

(A’s share of profit) : (B’s share of profit)= xp : yq.

3. Working and Sleeping Partners: A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.

## Basic Formulas for Partnership

If two partners A and B are investing their money to run a business then (Simple Partnership)

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

If two partners A and B are investing their money for different period of time to run a business then

(Compound Partnership)

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.

Shortcut Methods

### Rule 1:

If two partners are investing their money C1 and C2 for equal period of time and their total profit is P then their shares of profit are

If these partners are investing their money for different period of time
which is T1 and T2then their profits are

### Rule 2:

If n partners are investing their money C1, C2, …, Cn for equal period of time and their total profit is P then their shares of profit are

If these partners are investing their money for different period of time which
is T1, T2,… , Tthen their profits are

## Some Examples based on Partnership

Example - 1 : Anil, Mukesh and Ritesh started a business each investing Rs.20,000. After 4 month Anil withdraws Rs.6000, Mukesh withdraws Rs.8000, Ritesh invest Rs.6000 more At the end of the years, a total profit was Rs.65600. Find the share of Ritesh.
A. Rs. 20000
B. Rs. 28800
C. Rs. 17600
D. Rs. 19200
E. None Of These

Solution /Short tricks-
Ratio capital of Anil, mukesh and Ritesh.
= ( 20,000 x 4 + 14000 x 8 ) : ( 20,000 x 4 + 12000 x 8 ) : ( 20,000 x 4 + 26000 x 8 )
= 192000 : 176000 : 288000
Anil share = (65600 x 192 / 656 ) = 19200
Mukesh share = ( 65600 x 176 / 656 ) = 17600
Ritesh share = (65600 x 288 / 656 ) = 28800

Example - 2: Joy started a business and he invested in 76000, After some month, amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months amar join.
A. 4
B. 6
C. 8
D. 3
E. None Of These

Solution /Short tricks
Step 1: we can assume that amar join into business after x months.So amar money was invest into (12 – x ) months.
Step 2: 76000 x 12 / 57000 x ( 12 – x ) = 2 / 1
912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912 = x = 4
After 4 months amar join the business.

Example - 3:  Samir started a software business by investing Rs. 40,000 . After six months , Nitish Joined him with a capital of Rs. 60,000 . After 3 years , they earned a profit of Rs . 27,900 . What was Samir’s share in the profit ?
A. Rs. 12400
B. Rs. 13000
C. Rs. 13200
D. Rs. 15000
E. None Of These

Solution /Short tricks
: Samir : Nitish share of capital
= ( 40,000 x 36 ) : ( 60,000 x 30 ) = 1440000 : 1800000 = 4 : 5 .
Samir’s share is = Rs . 27900 x 4 / 9 = Rs. 12400.

Example - 4: Anil, Mukesh and Ritesh started a business by investing Rs. 125000 Rs. 150000 and Rs.175000 respectively. Find the share of Mukesh, out of an annual profit of Rs. 93,600..
A. Rs. 36400
B. Rs. 31200
C. Rs. 32500
D. Rs. 33200
E. None Of These

Solution /Short tricks
Ration of share Anil, Mukesh and Ritesh = Ratio of their investment
Anil : Mukesh : Ritesh = 125000 : 150000 : 175000 = 5 : 6 : 7
Anil share = Rs. [93600 x 5 / 18 ] = 26000.
Mukesh share = Rs. [93600 x 6 / 18 ] = 31200.
Ritesh share = Rs. [93600 x 7 / 18 ] = 36400

Example - 5: Jon and Harry started a partnership business investing some amount of money in the ratio of 2 : 3 . Ron joined them after six months with an amount equal to that of Harry . In what proportion should the profit at the end of one year be distributed among Jon , Harry and Ron ?
A. 5:3:4
B. 4:6:2
C. 5:3:2
D. 4:6:3
E. None Of These

Solution /Short tricks
Let the initial investment money ratio of Jon and Harry is 2x and 3x So Jon , Harry and Ron ratio of investment is ( Jon : Harry : Ron ) = (2x X 12 ) : ( 3x X 12 ) : ( 3x X 6 ) = 24 : 36 : 18 = 4 : 6 : 3

Example - 6: Manoj received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.120000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh?
A.Rs. 20000
B.Rs. 30000
C.Rs. 40000
D.Rs. 50000

Solution /Short tricks
Suppose Ramesh invested Rs. x. Then,
Manoj : Ramesh = 120000 * 6 : x *12.
720000/12x: 6000/3000
x = 30000

Example - 7: Yogesh started a business investing Rs. 45000. After 3 months, Pranab joined him with a capital of Rs. 60000. After another 6 months, Atul joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 20000. What would be Atuls share in it?
A.Rs 7000
B.Rs 6000
C.Rs 5000
D.Rs 4000
E. None Of These

Solution /Short tricks
Just take care of the months of investment, rest all will be simple.
Yogesh:Pranab:Atul = 45000*12:60000*9:90000*3 = 2:2:1
Atul's share = Rs. 20000 * (1/5) = Rs. 4000

Example - 8:  In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Rs 157300 was their profit, how much amount did B receive?
A.Rs 48000
B.Rs 47000
C.Rs 47400
D.Rs 48400
E. None Of These

Solution /Short tricks
A:B = 3:2 = 6:4
A:C = 2:1 = 6:3
A:B:C = 6:4:3
B share = (4/13)*157300 = 48400

Example - 9: Manoj got Rs.6000 as his share out of a total profit of Rs.9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.20,000 for 6 months, where as Ramesh invested his amount for the whole year, what was the amount invested by Ramesh ?
A. Rs.30000
B. Rs.40000
C. Rs.10000
D. Rs.5000
E. None Of These

Solution /Short tricks
Let the amount invested by Ramesh = Rs.x.Then, 20000×6 : 12x=6000:3000
or 12000012x=21 or x = 5000

Example - 10: Rs.700 is divided among A,B and C so that A receives half as much as B and B half as much as C. Then C's share is :
A. Rs.200
B. Rs.300
C. Rs.400
D. Rs.600
E. None Of These

Solution /Short tricks
Let C's share = Rs.x. Then
B's share = Rs.x2
And, A's share = Rs.x4
A:B:C = x4:x2:x=1:2:4

Hence, C's share = Rs.(700×47) = Rs.400
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