Partnership based problems

Two or more people doing business with the shared pool of resources and shared return on investment refers to Partnership and the one who invested can be considered as a partner.

There are many types of partners:
Active partner: The partner who manages the business.
Sleeping partner: The partner who just invests and doesn't work.


At the end of year profits or losses are distributed among partners in the ratio they invest.

If person A invests a₹ and person B invests b₹ for year in partnership, then at the end of year,

(A's share of profit or loss):(B's share of profit or loss) = a:b

If person A invests a₹ for x months and person B invests b₹ for y months in partnership, then at the end of year,
(A's share of profit or loss):(B's share of profit or loss) = ax : by


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Example 1:

Person A started a business with an investment of 7000, after 6 months person B joined A 6000, Find profit ratio at end of year.

solution:

Profit(A):Profit(B) = (12*7000):(6*6000)  {B invested for 6 months}

                               = 7:3

Example 2:

Person A commenced a business with an investment of 10,000 ,after 8 months person B joined A with x ,Find x such that their profit ratio at end of year becomes 1:1.

solution:

Profit(A):Profit(B) = (12*10,000):(4*x)    {B invested for 12-8=4 months}

1:1=1,20,000:4x
4x=1,20,000
x=30,000


Example 3:
A,B,C started a business and partnership,A initially invested 12000,added 3000 after 1 year,
B initially invested 3000,added 12000 after 2 years,

C initially invested 12000,added 4000 after 1 year,find ratios of their profits at the end of 3rd year
solution:
Profit(A):Profit(B):Profit(C)= (12000*1)+(15000*2):(3000*2)+(15000*1):(12000*1)+(16000*2)
                           =42000:21000:44000
                          =42:21:44
                       




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