# Partnership Questions

**FACTS AND FORMULAE FOR PARTNERSHIP PROBLEMS**

**Partnership: **When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.

**Ratio of Division of Gains:**

**(i)** When investments of all the partners are for the same time, the gain or loss is distributed a 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.

**(ii)** 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.

**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.

A) 11 : 13 : 15 | B) 11 : 13 : 17 |

C) 12 : 17 : 18 | D) 12 : 15 :16 |

Explanation:

Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.

A) 4000 | B) 5000 |

C) 6000 | D) 7000 |

Explanation:

A : B : C = 500 : 300 : 200 = 5 : 3 : 2.

Let their capitals be 5x, 3x and 2x respectively.

Then, 5x = 10000

=> x = 2000.

C's capital = 2x = Rs. 4000.

A) 22000 | B) 28000 |

C) 32000 | D) 36000 |

Explanation:

Suppose **B** invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.

So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.

B's profit : Total profit = 1 : 7.

Let the total profit be Rs. x Then, 1/7 = 4000/x or x = 28000.

A) 12000 | B) 12800 |

C) 13000 | D) 14500 |

Explanation:

Let the total profit be Rs. x. Then, B = 2x/7 and A = (x - 2x /7) = 5x / 7.

So, A : B = 5x/7 : 2x/7 = 5 : 2.

Let B s capital be Rs. y. Then, (16000 * 8) / ( y * 4) = 5/2 <=> (16000 * 8 * 2) / (5 * 4) = 12800..

A) Rs. 240 | B) Rs. 75 |

C) Rs. 125 | D) Rs. 354 |

Explanation:

The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)

=> 8:13

=> 8/21 x 630 = 240.

A) Rs. 39000 | B) Rs. 49000 |

C) Rs. 59000 | D) Rs. 69000 |

Explanation:

Interest received by A from B = 10% of half of Rs.50000 = 10% of Rs. 25000 = Rs.2500.

Amount received by A per annum for being a working partner = 1500 x 12 = Rs.18000

Let 'P' be the part of the remaining profit that A receives as his share.

So,total income of A = (Rs.2500 + Rs.18000 + Rs. P )

Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.

We know that income of A = Twice the income of B

So, (2500 + 18000 + P ) = 2(P)

P = 20500

Thus, the total profit = 2P + Rs.18000

= 2(20500) + 18000 = Rs.59000.

A) 12628 | B) 18245 |

C) 11235 | D) 10253 |

Explanation:

Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.

Reena's share Rs. 31570 * (2 / 5) = Rs. 12628.

A) 20000 | B) 40000 |

C) 60000 | D) 80000 |

Explanation:

Suppose Y invested Rs. y. Then 40000/y = 2/3 or y = 60000 .