Quantitative Aptitude: Partnership concepts & problems

Today, I am going to explain the concept of Partnership in Quantitative aptitude.

Partnership

Partnership is when two or more people pool in money as capital for a common venture. The profit of the venture is then divided among the people depending on the amount of money that each has invested. 

Different Investments, Same Time period of Investing

If the amount invested by the partners are C1 , C2 , C3  then the profit is distributed in the ratio C1  : C2  : C3

E.g. Rahul and Rohit get in Rs. 4000 and Rs. 5000 to fund a new venture. In what ratio should they divide the profit of Rs. 1,80,000 earned at the end of the year?

Profit has to be divided among Rahul and Rohit in the ratio of their investments i.e. 4 : 5

Let Rahul’s and Rohit’s share of profit be 4k and 5k respectively. The two share together would be the entire profit i.e. 4k + 5k = 1,80,000
i.e. 9k = 1,80,000 i.e. k = 20,000

Rahul’s share = 4 × 20,000 = 80,000

Rohit’s share = 5 × 20,000 = 1,00,000.

Same Investments, different Time periods

If the investments made by the partners are same, but the time period is different, the profit is divided in the ratio of the time periods.

When the investment and also the time period is different

Let there be three partners, one invests C1 for t1 time, second invests C2 for t2 time and third invests C3 for t3 time. The profit is shared in the ratio C1 × t1 : C2 × t2 : C3 × t3

E.g. A and B enter into a partnership with Rs. 8,000 and 15,000 respectively. After 3 months C joins them by investing Rs. 10,000. 4 months before the first year is completed, B quits, taking his invested amount back with him. In what ratio should the profit of Rs. 2,55,000 earned in the first year be distributed among the three?

A has invested 8,000 for 12 months.

B has invested 15,000 for 8 months.

C has invested 10,000 for 9 months. 

Thus the profit has to be distributed in the ratio of 8 × 12 : 15 × 8 : 10 × 9
i.e. 16 : 20 : 15  

A’s share = 16 × 2,55,000= 80,000

                     51

B’s share = 20 × 2,55,000= 1,00,000

                     51 

C’s share =  15 × 2,55,000= 75,000

                      51

When one partner has different amounts invested in different time periods

Let’s say in a partnership between A and B, A invests Rs. Ia for a time period of ta. But B invests Rs. Ib1 for a period of tb1 time and Rs. Ib2 for a period of tb2 time. In this case the profit will be divided between A and B in the ratio Ia × ta : (Ib1 × tb1 + Ib2 × tb2)

E.g. A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000 while at the end of second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of three years?

The profit has to be shared in the ratio of (40 × 3) : (80 × 1) + (40 × 2) : (120 × 2) + (40 × 1) i.e. 120 : 160 : 280 i.e. 3 : 4 : 7

Working Partner drawing a salary

In this case, first the salary of the partner is deducted from the profit & after that, whatever profit is left, is distributed among partners as we did in previous methods.

E.g. Two partners, A and B invest Rs. 10,000 and Rs. 15,000 in  a partnership firm which makes a profit of Rs. 50,000 at the end of the year. But since A is a working partner, he is entitled to a salary of Rs. 20,000 for the year. What is the amount that B receives?

The profit left after deducting A's salary = Rs. 50,000 – Rs. 20,000 = Rs. 30,000 

This amount will now be divided among A and B in the ratio of their investments i.e. in the ratio 10,000: 15,000 i.e 2: 3 

Thus, amount received by B =3/5th of Rs. 30,000 i.e. Rs. 18,000

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