Introduction:-
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.

There are two types of partnership.

1. Simple Partnership:  In simple partnership, capitals of partners are invested for the same period of time.

2. Compound Partnership:  In compound partnership, capitals of partners are invested for the different period of time.

Basic Formulas

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

Quiz On Partnership

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

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

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

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

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

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

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

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

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

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

TIME TAKEN:

Within 10 min          : EXCELLENT
10-14 min                : YOU CAN DO BETTER
More than 14 min    : YOU NEED TO WORK HARD

1.    (B):
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

2.    (A):
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.

3.    (A):
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.

4.    (B):
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

5.    (D):
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

6.    (B):
Suppose Ramesh invested Rs. x. Then,
Manoj : Ramesh = 120000 * 6 : x *12.
720000/12x: 6000/3000
x = 30000

7.    (D):
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

8.    (D):
A:B = 3:2 = 6:4
A:C = 2:1 = 6:3
A:B:C = 6:4:3
B share = (4/13)*157300  = 48400

9.    (D)
Let the amount invested by Ramesh = Rs.x.Then, 20000×6 : 12x=6000:3000
or 12000012x=21 or x = 5000

10.  (C)
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