# 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. 23,500 | B) Rs. 19,780 |

C) Rs. 21,700 | D) Rs. 20,050 |

Explanation:

Given **A & B in partnership**

A Invests 116000 for 12 months

=> A's share = 116000 x 12 = 13,92,000

B Invests for 6 months

=> B's share = 144000 x 6 = 8,64,000

Their Ratio = 1392 : 864 = 29 : 18

Let the Annual profit = P

Given B's share = Rs. 9000

=> 18/47 x P = 9000

=> P = 9000 x 47/18

=> P = 23,500

Hence, Overall profit = **P = Rs. 23,500**

A) 1564 | B) 1600 |

C) 1632 | D) 1714 |

Explanation:

Let O's share = **Rs. P**

=> N's share = $\frac{\mathbf{75}}{\mathbf{100}}\mathbf{}\mathbf{x}\mathbf{}\mathbf{P}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{3}\mathbf{P}}{\mathbf{4}}$

M's share = $\frac{\mathbf{5}}{\mathbf{4}}\mathbf{}\mathbf{x}\mathbf{}\frac{\mathbf{3}\mathbf{P}}{\mathbf{4}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{15}\mathbf{P}}{\mathbf{16}}$

$\frac{\mathbf{15}\mathbf{P}}{\mathbf{16}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{3}\mathbf{P}}{\mathbf{4}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{P}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4300}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\mathbf{P}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4300}\mathbf{}\mathbf{x}\mathbf{}\frac{\mathbf{16}}{\mathbf{43}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1600}$

A) Only a | B) Only c |

C) Both a & b | D) Data is not sufficient |

Explanation:

a. P's investment = (80000 x 6 + 60000 x 6) = 840000 for 1 month.

b & c. Q's investment = 80% of Rs. 60000 for 8 months.

= Rs.(48000 x 8) for 1 month = 384000 for 1 month

P : Q = 840000 : 384000 = 35 : 16.

But, the total profit is not given, so data is inadequate.

A) 2 months | B) 2.5 months |

C) 3 months | D) 3.5 months |

Explanation:

Ratio of profit of Rohith and Puneeth = 3600 x 12 : 2400 x P

= **3600 x 12/2400P = 2/1**

=> P = 9

So, Puneeth joined the business after (12 - P) = **12 - 9 = 3 months.**

A) Rs, 1109 | B) Rs. 1107 |

C) Rs. 1111 | D) Rs. 1113 |

Explanation:

From the given data,

K's profit : L's profit = 7x x 11 : 9x x 7

**= 11:9**

Therefore, L's profit =** 9 x 2460/20 = Rs. 1107**

A) Rs. 1250 | B) Rs. 600 |

C) Rs. 900 | D) Rs. 1500 |

Explanation:

From the given data,

Ratio of capital **= 12000 : 14400 = 5 : 6**

Required Difference =

$\frac{\mathbf{6}\mathbf{}\mathbf{-}\mathbf{}\mathbf{5}}{\mathbf{6}\mathbf{}\mathbf{+}\mathbf{}\mathbf{5}}\mathbf{}\left(\frac{\mathbf{88}}{\mathbf{100}}\mathbf{}\mathbf{x}\mathbf{}\mathbf{7500}\right)\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{12}}{\mathbf{100}}\mathbf{}\mathbf{x}\mathbf{}\mathbf{7500}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{1}{11}\mathrm{x}88\mathrm{x}75+12\mathrm{x}75\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=600+900\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{1500}$

A) 24000 | B) 16000 |

C) 12000 | D) 32000 |

Explanation:

Given Dileep and Narender started a business.

Dileep invested 8000 for 12 months

Let Narender invested 'p' for 6 months

At the end of the year, their profit ratio is 1 : 1.

Hence,

8000 x 12 : p x 6

p : 16000

p/16000 = 1/1

=> p = 16,000

Hence, Narender invested amount is **Rs. 16,000.**

A) Rs. 127 | B) Rs. 271 |

C) Rs. 721 | D) Rs. 217 |

Explanation:

ATQ,

P : Q = 5 : 12 = 10 : 24

Q : R = 4 : 5.5 = 24 : 33

P:Q:R = 10 : 24 : 33

Sum of the ratios = 10 + 24 + 33 = 67

Difference between the share of R & Q

= (33-24/67 x 2018)

= 9/67 x 2018

= Rs. 271.