# 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) 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) 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) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840 | B) Ram - Rs. 900, Raj - Rs. 800, Rakesh - Rs. 840 |

C) Ram - Rs. 840, Raj - Rs. 920, Rakesh - Rs. 840 | D) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 940 |

Explanation:

Initial investment of Ram = Rs.2500.

After 2 months he withdraw Rs.1250 from his capital.

Therefore, we have, Ram invested Rs.2500 for 2 months and Rs.(2500-1250=) 1250 for 4 months.

Raj invested Rs. 2250 for 3 months and Rs.(2250-750=) 1500 for 3 months.

And, Rakesh invested Rs.3500 for 3 months;

Their investing ratio:

Ram:Raj:Rakesh = (2500x2 + 1250x4):(2250x3 + 1500x3):(3500x3)

= (10,000):(11,250):(10,500) = 1000:1125:1050 = 40:45:42

Total profit for 6 months = Rs.2540

Therefore, Ram's share = Rs.(2540 x 40/(40+45+42)) = Rs.(2540 x 40/127) = Rs.800

Raj's share = Rs.(2540 x 45/127) = Rs.900

Rakesh's share = Rs.(2540 x 42/127) = Rs.840

A) 3500 | B) 3600 |

C) 3700 | D) 3800 |

Explanation:

A : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)

= 147 : 189 : 126

= 7 : 9 ; 6.

Difference of B and C's shares = Rs. ( 26400 * 9/22 - 26400 * 6/22 ) = Rs. 3600.

A) 11/3 | B) 2/13 |

C) 3/11 | D) 13/4 |

Explanation:

Let Veena paid x,

so Akshitha paid 2x/3 , and Lasya paid 2x,

So total bill paid is given by

x+(2x/3) +2x = 1, we get

i.e. x = 3/11

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) 64 | B) 76 |

C) 84 | D) 98 |

Explanation:

Given total sum = Rs. 427

And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.

=> 3A = 4B = 7C

But given

=> A + B + C = 427

Now express A and B in terms of C i.e

=> (7C/3) + (7C/4) + C = 427

=> C = 84

A) 11 months | B) 9 months |

C) 7 months | D) 10 months |