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:

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 8822
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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7 8712
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 8185
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 7627
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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9 7182
Q:

The ratio of investments of two partners is 11:12 and the ratio of their profits is 2 : 3. If A invested the money for 8 months , find for how much time B invested his money.

Answer

Suppose A invested Rs.11 for 8 months and B invested Rs. 12 for x months.


\inline \therefore Ratio of investments of A and B


                  = (11 x 8) : (12 x x)


                  = 88 : 12x 


\inline \therefore \inline \frac{88}{12x}=\frac{2}{3}\Rightarrow x=11

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13 6808
Q:

Karan started a business investing Rs 29000. After five months, Satish joined with a capital of Rs 18000. If at the end of the year, they earn a profit of Rs. 16970, then what will be the share of Satish in the profit ?

A) Rs. 5422 B) Rs. 5489
C) Rs. 4511 D) Rs. 6145
 
Answer & Explanation Answer: C) Rs. 4511

Explanation:

Now as per question, Karan invested for 12 months and Satish invested for 7 months.

So, Karan:Satish = (29000 x 12):(18000 x 7)

= 348:126

= 58:21

 

Satish Ratio in profit will be= 16970×2179 = Rs. 4511

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5 6691
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 6617