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.

Q:

Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?

A) Rs. 45,000 B) Rs. 50,000
C) Rs. 70,000 D) Rs. 75,000
 
Answer & Explanation Answer: B) Rs. 50,000

Explanation:

Sekar: Rajeev: jatin = (25000×12+35000×12+45000×12):(35000×24) : (35000×12)

                            = 1260000 : 840000 : 420000

                            = 3 : 2 : 1.

 

Rajeev's Share =Rs.(150000×2/6)

                      =Rs.50000.

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30 25348
Q:

Aman started a business investing Rs. 70,000. Rakhi  joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?

A) 11 : 13 : 15 B) 11 : 13 : 17
C) 12 : 17 : 18 D) 12 : 15 :16
 
Answer & Explanation Answer: D) 12 : 15 :16

Explanation:

Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.

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29 44292
Q:

A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?

A) 2 : 3 : 5 B) 3 : 4 : 7
C) 5 : 6 : 4 D) 1 : 3 : 5
 
Answer & Explanation Answer: B) 3 : 4 : 7

Explanation:

A : B : C  = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)

= 144 : 192 : 336

= 3 : 4 : 7.

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28 26791
Q:

Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?

A) 10110 B) 10500
C) 12000 D) 13000
 
Answer & Explanation Answer: B) 10500

Explanation:

Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.

Simran's share = Rs. ( 24500 * 3/7)  =  Rs. 10500.

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27 29007
Q:

A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit  of Rs. 35,000, A receives :

A) 14700 B) 15000
C) 12000 D) 13500
 
Answer & Explanation Answer: A) 14700

Explanation:

Let C = x. Then, B = x + 5000  and A =  x + 5000 + 4000 = x + 9000.

So,  x + x + 5000 + x + 9000 = 50000  <=>  3x = 36000  <=>

x = 12000.

A : B : C =  21000 : 17000 : 12000 = 21 : 17 : 12.

A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.

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25 22977
Q:

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?

A) 144 B) 169
C) 225 D) 339
 
Answer & Explanation Answer: A) 144

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.

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24 16025
Q:

Reena and Shaloo are partners in a business, Reena invests Rs, 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months, out of a profit of  Rs. 31,570, Reena's share is :

A) 12628 B) 18245
C) 11235 D) 10253
 
Answer & Explanation Answer: A) 12628

Explanation:

Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.

Reena's share Rs. 31570 * (2 / 5) = Rs. 12628.

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23 31003
Q:

A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

A) Rs. 7500 B) Rs. 8000
C) Rs. 8500 D) Rs. 9000
 
Answer & Explanation Answer: D) Rs. 9000

Explanation:

Let B's capital be Rs. x

 

Then,3500×127x=23

=> 14x = 126000 

=> x = 9000.

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23 23776