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 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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Q:

A is a working and B is sleeping partners in a business. A puts in Rs. 5000 and B puts in Rs.6000. A receives % of the profit for managing the business and the rest is divided in proportion to their capital. What does each get out of a profit of Rs. 880?

Answer

Total profit = Rs. 880


A's share for managing the business i.e 


\inline 12\frac{1}{2} %  =  \inline \frac{25\times 880}{200}=Rs.110


Remaining profit of A and B as per their capital = 880 - 110 = Rs. 770


Ratio of amounts = 5000 : 6000 = 5 : 6


Sum of ratios = 5 + 6 = 11


A's share = \inline 770\times \frac{5}{11}= Rs.350


A's total share = 350 + 110 = Rs. 460


B's share = \inline 770\times \frac{6}{11}=Rs.420

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12 5837
Q:

If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive ____

A) Rs.700 B) Rs.800
C) Rs.900 D) Rs.1000
 
Answer & Explanation Answer: C) Rs.900

Explanation:

Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6,  and C =k/10 .

 

A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.

 

Hence, C's share (4650 *  6/31) = Rs, 900.

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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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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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