# 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) 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) 48400 | B) 54200 |

C) 64000 | D) 74000 |

Explanation:

A : B = 3 : 2 => B : A = 2 : 3 = 4 : 6 and A : C = 2 : 1 = 6 : 3.

So, B : A : C = 4 : 6 : 3 or A : B : C = 6 : 4 : 3.

B's share = Rs. (157300 x 4/13 ) = Rs. 48400.

A) Only c is sufficient | B) Both a & b are sufficient |

C) Both A & B gives result | D) None |

Explanation:

a and b give, profit after 3 years = Rs.(3/8 x 22000) = Rs.8250.

From c also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

∴ P's share = Rs.(8250 x 5/11) = Rs. 3750.

Thus, (either C is redundant) or (a and b are redundant).

A) 8400 | B) 8200 |

C) 8100 | D) 8000 |

Explanation:

Ratio of their shares = 22500 : 35000 = 9 : 14.

Deepak's share = Rs. (13800 * 14/23) = Rs. 8400.

A) Rs. 4000 | B) Rs. 6000 |

C) Rs. 9000 | D) Rs. 3000 |

Explanation:

Given ratio of initial investments = $\frac{7}{2}:\frac{4}{3}:\frac{6}{5}$ = 105 : 40 : 36.

Let the initial investments be 105x, 40x and 36x.

$\therefore A:B:C=\left(105x\times 4+\frac{150}{100}\times 105x\times 8\right):\left(40x\times 12\right):\left(36x\times 12\right)$

= 1680x : 480x : 432x = 35 : 10 : 9.

Hence, B's share = $\left(21600\times \frac{10}{54}\right)$ = Rs. 4000.

A) Rs. 1100 | B) Rs. 500 |

C) Rs. 1200 | D) Rs. 700 |

Explanation:

Let the amounts to be received by P, Q and R be p, q and r.

p + q + r = 1200

p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200

=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200

=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.

A) 4:6:8 | B) 4:7:8 |

C) 4:8:16 | D) 4:9:16 |

Explanation:

Let their investments be Rs. x for 12 months, Rs. y for 8 months and Rs. z for 6 months respectively.

Then, 12x : 8y : 6z = 4 : 6 : 8

Now, 12x/8y = 4/6 <=> 9x=4y <=> y=9x/4

And, 12x/6z = 4/8 <=> 4x=z <=> z=4x

Therefore, x : y: z = x : 9x/4: 4x = 4 : 9 : 16

A) 17:23 | B) 17:3 |

C) 17:33 | D) 3:4 |