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 hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were :

A) 150 B) 160
C) 170 D) 180
 
Answer & Explanation Answer: B) 160

Explanation:

A : B : C = 7 : 8 : 11.

Hire charges paid by B = Rs. (520 *  8/26) = Rs. 160.

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10 11748
Q:

In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive ?

A) 48400 B) 54200
C) 64000 D) 74000
 
Answer & Explanation Answer: A) 48400

Explanation:

A : B = 3 : 2 => B : A = 2 : 3 = 4 : 6 and A : C = 2 : 1 = 6 : 3.

So, B : A : C = 4 : 6 : 3 or A : B : C = 6 : 4 : 3.

B's share = Rs. (157300 x 4/13 ) = Rs. 48400.

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11 11104
Q:

A,B and C enter into a partnership in the ratio  72:43:65. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs. 21600, then B's share in the profit is :

A) Rs. 4000 B) Rs. 6000
C) Rs. 9000 D) Rs. 3000
 
Answer & Explanation Answer: A) Rs. 4000

Explanation:

Given ratio of initial investments = 72:43:65 = 105 : 40 : 36.

 Let the initial investments be 105x, 40x and 36x.

 

A:B:C = 105x×4 + 150100×105x×8 : 40x×12 : 36x×12  

               = 1680x : 480x : 432x = 35 : 10 : 9.

 

Hence, B's share = 21600×1054 = Rs. 4000.

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13 10053
Q:

Three friends, P, Q and R started a partnership business investing money in the ratio of 5 : 4 : 2 respectively for a period of 3 years. What is the amount received by P as his share in the total profit ?

a. Total amount invested in the business in Rs. 22,000.

b. Profit earned at the end of 3 years is 3/8 of the total investment.

c. The average amount of profit earned per year is Rs. 2750.

A) Only c is sufficient B) Both a & b are sufficient
C) Both A & B gives result D) None
 
Answer & Explanation Answer: C) Both A & B gives result

Explanation:

a and b give, profit after 3 years = Rs.(3/8 x 22000) = Rs.8250.

From c also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

∴ P's share = Rs.(8250 x 5/11) = Rs. 3750.

Thus, (either C is redundant) or (a and b are redundant).

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3 9731
Q:

P and Q started a business investing Rs, 85,000 and Rs. 15,000 respectively. In what ratio the profit named after 2 years bo divided between P and Q respectively ?

A) 17:23 B) 17:3
C) 17:33 D) 3:4
 
Answer & Explanation Answer: B) 17:3

Explanation:

P : Q = 85000 : 15000 = 86 : 15 = 17 : 3 .

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11 9368
Q:

Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?

A) Rs. 1100 B) Rs. 500
C) Rs. 1200 D) Rs. 700
 
Answer & Explanation Answer: B) Rs. 500

Explanation:

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.

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10 9184
Q:

A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A ?

A) Rs. 240 B) Rs. 75
C) Rs. 125 D) Rs. 354
 
Answer & Explanation Answer: A) Rs. 240

Explanation:

The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)

=> 8:13

=> 8/21 x 630 = 240.

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9 9131
Q:

Three partners shared the profit in a business in the ratio 4:6:8. They had partnered for 12 months, 8 months and 6 months respectively. What was the ratio of their investments?

A) 4:6:8 B) 4:7:8
C) 4:8:16 D) 4:9:16
 
Answer & Explanation Answer: 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

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11 8886