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:

A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

A) Rs. 45 B) Rs. 50
C) Rs. 55 D) Rs. 60
 
Answer & Explanation Answer: A) Rs. 45

Explanation:

A:B:C = (10×7):(12×5):(15×3)

         = 70 :60 :45

         = 14 :12 :9

 

C's rent = Rs.(175×9/35)

            =Rs. 45.

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9 10976
Q:

A and B started a business jointly A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is :

A) 22000 B) 28000
C) 32000 D) 36000
 
Answer & Explanation Answer: B) 28000

Explanation:

Suppose B invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.

So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.

B's profit : Total profit  = 1 : 7.

Let the total profit be Rs. x Then,  1/7 = 4000/x  or x = 28000.

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12 9885
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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9 9831
Q:

A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :

A) 4000 B) 5000
C) 6000 D) 7000
 
Answer & Explanation Answer: A) 4000

Explanation:

A : B : C = 500 : 300 : 200 = 5 : 3 : 2.

Let their capitals be 5x, 3x and 2x respectively.

Then, 5x = 10000  

=>  x = 2000.

C's capital = 2x = Rs. 4000.

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14 8937
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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10 7925
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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9 7509
Q:

X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is :

A) 20000 B) 40000
C) 60000 D) 80000
 
Answer & Explanation Answer: C) 60000

Explanation:

Suppose Y invested Rs. y. Then 40000/y = 2/3 or y = 60000 .

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5 7438
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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10 7384