# 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) Rs. 45 | B) Rs. 50 |

C) Rs. 55 | D) Rs. 60 |

Explanation:

A:B:C = (10×7):(12×5):(15×3)

= 70 :60 :45

= 14 :12 :9

C's rent = Rs.(175×9/35)

=Rs. 45.

A) 10110 | B) 10500 |

C) 12000 | D) 13000 |

Explanation:

Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.

Simran's share = Rs. ( 24500 * 3/7) = Rs. 10500.

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) 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) 2 : 3 : 5 | B) 3 : 4 : 7 |

C) 5 : 6 : 4 | D) 1 : 3 : 5 |

Explanation:

A : B : C = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)

= 144 : 192 : 336

= 3 : 4 : 7.

A) 144 | B) 169 |

C) 225 | D) 339 |

Explanation:

Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

Let their initial investments be 6x, 2x and 3x respectively.

A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.

B's share = Rs. (378*8/21) = Rs. 144.

A) Rs. 45,000 | B) Rs. 50,000 |

C) Rs. 70,000 | D) Rs. 75,000 |

Explanation:

Sekar: Rajeev: jatin = (25000×12+35000×12+45000×12):(35000×24) : (35000×12)

= 1260000 : 840000 : 420000

= 3 : 2 : 1.

Rajeev's Share =Rs.(150000×2/6)

=Rs.50000.