# 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) 500 | B) 1000 |

C) 1500 | D) 2000 |

Explanation:

Let the total profit be Rs. 100.

After paying to charity, A's share = (95*3/5) = Rs. 57.

If A's share is Rs. 57, total profit = Rs. 100.

If A's share is Rs. 855, total profit = (100/57*855) = 1500.

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) 1 : 2 : 3 | B) 3 : 4 : 15 |

C) 3 : 5 : 10 | D) 5 : 6 : 10 |

Explanation:

Let their initial investments be x, 3x and 5x respectively. Then,

A:B:C = (x*4+2x*8) : (3x*4+(3x/2)*8) : (5x*4+(5x/2)*8)

20x : 24x : 40x = 5 : 6 : 10

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) 4 months | B) 5 months |

C) 6 months | D) 8 months |

Explanation:

Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

A) Rs.700 | B) Rs.800 |

C) Rs.900 | D) Rs.1000 |

Explanation:

Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .

A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.

Hence, C's share (4650 * 6/31) = Rs, 900.

A) 3 months | B) 6 months |

C) 10 months | D) 12 months |

Explanation:

Let the total profit be Rs. z. Then,

B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.

A : B = z/3 : 2z/3 = 1:2

Let the total capital be Rs, X and suppose B's money was used for x months. Then.

(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .

Thus, B's money was used for 10 months.