Partnership

Hello Readers,

We shall discuss about Partnership of the Quant section.  Now a days these topics  have became an important part of the Quant test in not only SSC but also almost all Entrance Exams like FCI Exams and IBPS Exam.So Here we will help you in this.We will  provide short notes and quant quiz.

What is Partnership?

Partnership: Persons  two or more than two persons when start and run the new  a business  jointly of there own choice, the persons start they are called partners and the deal is done between the partners is known as partnership.

Ratio of Divisions of Gains:
1. When investments of all the partners are for the same time, the gain or loss is distributed 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.

2.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.

3. 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.

1. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

A. 5 : 7 : 8

B. 20 : 49 : 64

C. 38 : 28 : 21

D. None of these

2.  P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share?

A. 114

B. 120

C. 134

D. 144

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

A. Rs. 8400

B. Rs. 11,900

C. Rs. 13,600

D. Rs. 14,700

4. 29. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?

A. 18:19:19

B. 18:18:19

C. 19:19:18

D. 18:19:19

5. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

A. Rs. 7500

B. Rs. 9000

C. Rs. 9500

D. Rs. 10,000

6. 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 157300 was their profit, how much amount did B receive?

A. 48000

B. 48200

C. 48400

D. 48600

6. 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

7. If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive

A. 600

B. 700

C. 800

D. 900

8. Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.

A. 4000

B. 5000

C. 6000

D. 7000

9. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is

A. 40000

B. 50000

C. 60000

D. 70000

10. Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?

A. Rs 2380

B. Rs 2300

C. Rs 2280

D. Rs 2260

ANSWERS AND SOLUTION :
1(B)Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x/8y  = 5/7  =>  98x = 40y   =>  y = 49/20 x
And, 14x/7z = 5/8 =>  112x = 35z    => z = 112/35 x = 16/5 .x.
So  x : y : z  =  x : 49/20 x : 16/5 x = 20 : 49 : 64.

2(D)Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
B's share = 378 * (8/21) = 18 * 8 = 144

3(D)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.
So  A's share = Rs. (35000 x 21/50) = Rs. 14,700.

4(C)Explanation :
P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)
= 95 : 95 : 90
= 19 : 19: 18

5(A)Explanation:
A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
So  B's share = Rs. (25000 x 3/10) = Rs. 7,500.

6(C)Explanation :
Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 * 4/(6+4+3) = 157300*4/13
= 12100*4 = 48400

6(A)Explanation:
A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs.(175 x 9/35) = Rs. 45.

7(D)Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 * (6/31) = 150*6 = 900

8(C)Explanation :
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000

9(C)Explanation :
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000

10(A)Explanation:
Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So  Kamal: Sameer = (9000*12):(8000*7)
= 108 : 56
=  27 : 14
Sameer Ratio in profit will be  =(6970*14/41)=Rs2380

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