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**PARTNERSHIP**

When two or more than two persons run a business jointly, they are called partners and the deal is known as a partnership.

**CONCEPT OF PARTNERSHIP**

- 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.

**Type Of questions Asked For :**

- Share in total profit
- Profit ratio
- Time
- Capital

**Ex: In a business A, B and C are invested Rs. 380, Rs. 400, and 420 respectively. Divide a net profit of Rs. 180 among the partners.**

**Sol: **A’s profit: B’s profit: C’s profit = A : B : C

= 380 : 400 : 420

= 19 : 20 : 21

Profit share of A = = 57 Rs.

Profit share of B = = 60 Rs.

Profit share of C = = 63 Rs.

**Ex: A, B and C started a business by investing Rs. 120000 Rs. 135000 and Rs. 150000 respectively. If the difference between the profit of A & B is Rs 2100. Find the total profit.**

**Sol:** Ratio of shares of A, B & C = Ratio of their investment

A : B : C = 120000 : 135000 : 150000

= 8 : 9 : 10

Difference b/w (A & B) = 9 - 8 = 1

1 = 2100

Total profit (8+9+10) = 27

= 27 x 2100

= Rs 56700

**Ex: P, Q, and R started a business with investing their money in the ratio of 1 : 2 : 4, after 6 months P invested the half amount more as before and Q invested twice the amount as before while R withdrew 1/4th of their investments. Find the ratio of their profits at the end of the year?**

**Sol:**

Ratio = P : Q : R

= (1 x 6 + x 6) : (2 x 6 + 4 x 6) : (4 x 6 + 3 x 6)

= 5 : 12 : 14

**Ex: Two companies A and B entered into a partnership just 5 months ago. The ratio of profit claimed by A and B is 6 : 17. If B had just started his business 12 months ago with Rs.1275, what is the amount contributed by A?**

**Sol:**

A =

= Rs.1080

**Ex: A, B and C start a business each investing Rs. 20,000. After 5 months A withdraws Rs. 5000, B withdraws Rs. 4000 and C invest Rs. 6000 more. At the end of the year, the total profit of Rs. 69,900. Find the share of each.**

**Sol:** Ratio of the capitals of A, B and C.

= (20,000 × 5 + 15000 × 7) : (20000 × 5 + 16000 × 7) : (20000 × 5 + 26000×7)

= 20,5000 : 212000 : 282000

= 205 : 212 : 282

A’s share = 69900 × = 20500 Rs

B’s share = 69900 × = 21200 Rs

C’s share = 69900 × = 28200 Rs

**Ex: A invested Rs. 76000 in a business. After few months, B joined him with Rs. 57000. At the end of the year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join ?**

**Sol: **Let B joined after x months.

Then B’s money was invested for (12 – x) months

A B

76000 x 12 : 57000 x (12 – x)

76 x 12 : 57 (12 – x )

912 = 114 (12 - x)

8 = 12 - x

x = 4

Hence, B joined after 4 months.

**Ex: A and B are partners in a business. They invest in the ratio of 5 : 6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B's investment was used?**

**Sol:**

ratio = A : B

= 5 x 8 : 6 x t

according to the question,

5 x 8 : 6 x t = 5 : 9

t = 12 months

**Ex: In a partnership, A invests of 1/6**** the capital for 1/6**** of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for whole time. Find A’s share out of the total profit of Rs. 2300.**

**Sol:** Capital of C = 1 -

Let the total time be 1 year.

A’s profit : B’s profit : C’s profit = A : B : C

= 1 : 4 : 18

Share of A = = Rs. 100

**Ex.: ****A is working and B is a sleeping partner in a business. A puts in Rs.5,000 and B puts in Rs.6,000. A receives ****% of the profit for managing the business and the rest is divided in proportion of their capitals. What does each get out of a profit of Rs.880?**

**Sol: **The amount which A receives for managing

of Rs.880 = ×880 = Rs.110

The amount left = 880 – 110 = Rs.770

The amount left is to be divided in the ratio = 5,000 : 6,000 = 5:6

Out of the amount left, A’s share =

Out of the amount left, B’s share =

Total share receive by A = 110 + 350 = Rs.460

Share received by B = Rs.420

**Ex.: A, B and C invested capitals in the ratio of 2:3:5. At the end of the business terms, they received the profit in the ratio of 5:3:12. Find the ratio of time for which they contributed their capitals ?**

**Sol: **Here, P1: P2: P3 = 5 : 3 : 12

and x1: x2: x3= 2 : 3 : 5

The required ratio

= : 1×10:

= 25 : 10 : 24

**Ex.: A starts a business with Rs.4000 and B joins the business 4 months later with an investment of Rs.5000. After a year, they earn a profit of Rs.22000. Find the shares of A and B.**

**Sol: **A’s share : B’s Share

= 4000 × 12 : 5000 × (12 - 4)

= 4 × 12 : 5 × 8 = 6 : 5

Now, let the share of A = 6x

and the share of B = 5x

According to the question,

6x + 5x = 22000

11x = 22000

x = Rs. 2000

Share of A = 6x = 6 × 2000 = Rs. 12000

and share of B = 5x = 5 × 2000 = Rs. 10000

**Ex.: In a business partnership among A,B,C and D, the profit is shared as follows. ** **= 1/3. If the total profit is ****Rs.400000, the share of C is-**

**Sol: Given, **

A : B = 1 : 3

B : C = 1 : 3

C : D = 1 : 3

A : B : C : D = 1 × 1 × 1 : 3 × 1 × 1 : 3 × 3 × 1 : 3 × 3 × 3 = 1 : 3 : 9 : 27

Let the profits of A,B,C and D are x, 3x, 9x and 27x respectively.

Partnership of C = × 400000

**Ex.: Alok, Bhism and Chandra hired a meadow jointly for the whole year. Alok put in 80 buffaloes for 10 months, Bhism 100 buffaloes for 5 months and Chandra 150 buffaloes for 4 months. If Alok paid Rs.320 as rent, what is the total rent for the meadow?**

**Sol: **Number of buffaloes put by Alok for 1 month

= 10 × 80 = 800

Number of buffaloes put by Bhisma for 1 month

= 5 × 100 = 500

and number of buffaloes put by Chandra for 1 month

= 4 × 150 = 600

Ratio = 800 : 500 : 600

= 8 : 5 : 6

Sum of ratios = 8 + 5 + 6 = 19

Total rent for the meadow =

= Rs. 760

**Ex.: A, B and C started a business by investing Rs.40500, Rs.45,000 and Rs.60,000, respectively. After 6 months C withdrew Rs.15,000 while A invested Rs.4500 more. In annual profit of Rs.56,100 the share of C will exceed that of A by?**

Sol: Ratio of equivalent capitals of A, B and C for 1 month

(40500 × 6 + 45000 × 6) : (45000 × 12)

: (60000 × 6 + 45000 × 6)

(405 + 450) : (450 × 2) : (600 + 450)

= 855 : 900 : 1050

= 171 : 180 : 210

= 57 : 60 : 70

Sum of ratios = 57 + 60 + 70 = 187

Required difference = × 56100

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