**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