# 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 months | B) 9 months |

C) 7 months | D) 10 months |

A) Rs.2010 | B) Rs.2200 |

C) Rs.2000 | D) Rs.2100 |

Explanation:

Let money invested by Raghu = Rs. x

Money invested by Trishul = 9/10 x = 0.9x

Money invested by Vishal = 9/10x * 110/100 = 0.99x

Also, x+0.9x+0.99x = 5780

= x= 5780/2.89 = 2000

Therefore, amount invested by Raghu is Rs. 2000.

A) 4530 | B) 4440 |

C) 4360 | D) 4280 |

Explanation:

Ratio of shares of A,B,C = (24 x 4) : (10 x 6) : (56 x 5)

= 96 : 60 : 280.

Let total rent be Rs. x. Then, A's share = $Rs.\frac{96x}{436}$

$\therefore \frac{96x}{436}=960\iff x=\frac{960\times 436}{96}=4360$

Hence total rent of the field is Rs. 4360.

A) Rs. 820 | B) Rs. 830 |

C) Rs. 840 | D) Rs. 850 |

Explanation:

Let the total amount in the partnership be 'x'.

Then A's share = x/3

B's share = x/4

C's share = x/5

D's share = x - (x/3 + x/4 +x/5) = 13x/60

A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13

A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830.

A) Rs. 75,000 | B) Rs. 85,000 |

C) Rs. 98,000 | D) Rs. 1,00,000 |

Explanation:

Deepa invested Rs.50,000 for 12 months, Rs.(50000 + 20000) for 12 months and Rs.(50000 + 20000 + 20000) for 12 months.

i.e, she invested Rs.50,000 for 12 months, Rs.70000 for 12 months and Rs.90000 for 12 months.

Sushma invested Rs. 70000 for 2 years; i.e, Rs.70000 for 24 months

And, Avanthi invested Rs.70000 for 1 year; i.e, Rs. 70000 for 12 months.

Their investing ratio:

Deepa : Sushma : Avanthi = (50,000 x 12 + 70000 x 12 + 90000 x 12):(70000 x 24):(70000 x 12)

= (25,20,000):(16,80,000):(8,40,000) = 252:168:84 = 3:2:1

Total profit for 3 years = Rs.3,00,000

Therefore, Sushma's share = Rs.(3,00,000 x 2 /(3+2+1)) = Rs.(3,00,000 x 2/6) = Rs.1,00,000.

A) 12,421 | B) 9,423 |

C) 11,600 | D) 10,500 |

Explanation:

The ratio of their investments:

50000x36 : 80000x30 = 3 : 4

Simran's share of profit = (24500x3/7) = Rs.10,500.

A) Rs. 8,640 | B) Rs. 9,850 |

C) Rs. 10,000 | D) Rs. 11,220 |

Explanation:

Ratio of investments of A, B & C = 2×6+4×6 : 3×12 : 4×12

= 36 : 36 : 48

= 6 : 6 : 8

But given that the annual profit of B is Rs. 3000

=> 6 ratio = 3000

Then for the total annual profit of partners is

20 ratio = 3000 x 20/6 = 10,000.

A) 50000 | B) 48000 |

C) 38000 | D) 40000 |

Explanation:

Here from the given information,

The ratio of investments of Rajeev, Deepu & Shakti is

R : D : S = (10000 × 12) : (12000 × 10) : (7200 × 8)

= 25 : 25 : 12

Now the Profit = 2 × (72000-10000) = 124000

Share of Rajeev = 124000 x 25/62 = 48000

Profit of Rajeev = 48000 - 10000 = 38000