## Partnership

**Important terms:**

**1) Partnership:**If two or more than two persons run a business jointly, then they are called partners and the deal is known as partnership. There are two types of partnership: simple partnership and compound partnership.

**2) Simple partnership:**

a) In this type of partnership, the capitals of each of the partners are invested for same time.

b) Gains or losses are divided among the partners in the ratio of their investments.

**3) Compound partnership:**

a) In this type of partnership, the periods of investments are unequal.

b) Equivalent capitals for a unit of time are calculated by multiplying the capital with number of units it was in business.

**4) Working partner:**Partner managing the business

**5) Sleeping partner:**Partner investing money

**Quick tips and tricks:**

**Ratio of division of gains:**

**1) Simple partnership:**Partners invest for same time.

Suppose P and Q invest Rs. x and Rs. y respectively for a year in a business, at the end of the year:

P’s share of profit | = | x |

Q’s share of profit | y |

x : y = P’s share of profit : Q’s share of profit

**2) Compound partnership:**When partners invest for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time).

Suppose P and Q invest Rs. x for a months and Rs. y for b months respectively then,

P’s share of profit | = | xa |

Q’s share of profit | yb |

**Capital (amount) of P x Time period of P: Capital (amount) of Q x Time period of Q = P’s share of profit : Q’s share of profit**

When n number of partners invests for different time periods T, then

**A**

_{1}T_{1}: A_{2}T_{2}: A_{3}T_{3}……: AnTn = P_{1}: P_{2}: P_{3}....: P_{n}A is the amount, T is the time period and P is the profit earned.

**Question Variety**

Type 1: Simple Partnership:

a) 2 partners join at same time to start a business

b) 3 partners join at same time to start a business

**a) Two Partners Join at Same Time to Start a Business:**

Note: Different cases/types: The questions are twisted in exams in the following different forms shown below:

**Q 1.**Smith and Kate started a business investing Rs. 84,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between Smith and Kate respectively?

a. 2 : 3

b. 3 : 1

c. 13 : 3

d. None of these

View solution

Correct Option: (b)**Hint: **

P’s share of profit | = | x | - - - - - - (x and y are investments) |

Q’s share of profit | y |

x : y = P’s share of profit : Q’s share of profit

Therefore,

Smith’s share of profit | = | 84000 | = | 3 |

Smita’s share of profit | 28000 | 1 |

**Q 2.**Sham and Ram invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Sham invested Rs. 40,000, then what was the amount invested by Ram?

a. Rs. 30,000

b. Rs. 45,000

c. Rs. 60,000

d. Rs. 75,000

View solution

Correct Option: (c)**Hint:**

P’s share of profit | = | x | - - - - - - (x and y are investments) |

Q’s share of profit | y |

Let the amount invested by Ram be Rs. X

Therefore,

Sham’s share of profit | = | Sham’s investment |

Ram’s share of profit | Ram’s investment |

2 | = | 40000 |

3 | X |

**Amount invested by Ram = Rs. 60,000**

**b) Three partners join at same time to start a business**

**Q 3.**John, Tyson and Mike started a business by investing Rs.1,00,000, Rs. 1,50,000 and Rs. 1,75,000 respectively. Find the share of Mike, out of an annual profit of Rs. 46,000.

a. Rs. 15941. 93

b. Rs. 16943. 59

c. Rs. 18941. 17

d. Rs. 19971. 03

View solution

Correct Option: (c)**Here, three partners invest together and earn a profit of Rs. 46,000 at the end. ****Hint: **Ratio of shares of John, Tyson and Mike = Ratio of their investments

Therefore, **100000 : 150000 : 175000 = 4 : 6 : 7**

Now, we have to calculate share belonging to each person from all the shares considering the annual profit.

Total shares = 4 + 6 + 7 = 17 shares

John’s Share = | 4 | × 46000 = Rs. 10823.53 |

17 |

Tyson’s Share = | 6 | × 46000 = Rs. 16235.294 |

17 |

Mike’s Share = | 7 | × 46000 = Rs. 18941.176 |

17 |

**Q 4.**Harry, John and Smith start a shop by investing Rs. 27,000. Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profit was distributed among them and Smith earns the share of Rs. 36,000. Find the total profit.

a. Rs. 1,10,000

b. Rs. 1,2,5000

c. Rs. 98,000

d. Rs. 80,000

View solution

Correct Option: (d)**Hint: **Ratio of shares of Harry, John and Smith = Ratio of their investments**Harry : John : Smith = 27000 : 72000 : 81000 = 3 : 8 : 9 ****Given: ** Share of profit earned by Smith = Rs. 36,000

Total no. of shares = 3 + 8 + 9 = 20 shares

Smith’s share = | 9 |

20 |

36000 | = | 9 |

X | 20 |

X = | 36000 × 20 | = 80000 |

9 |

**Total profit = Rs. 80,000**