**Partnership**

Hello all, In my previous blog we have seen **ratio and portion** concept https://www.sevenmentor.com/blog/ratio-and-proportion/ based on this I will discuss one of its application i.e. Partnership, from which questions may asked in almost all competitive exams.

Partnership is refers to an agreement or deal between two or more persons who makes a deal and invest of money for running a business and after certain time they agree to share receive profits or loss in the ratio of their invested money and time period, then such a group of persons is known as partner and the deal between them is known as partnership.

** Partners are of two types:-**

(1) **Working partner: – **A person/partner who invests their money in business and also actively manage the work of a company or firm and also get a salary for his/her work is known as a working partner.

(2) **Sleeping partner: –** A person/partner who invests their money in business but not actively manages the work of the company or firm and gets only share in profit is known as a sleeping partner.

**Types of Partnership:-**

**Simple partnership.**

If the investment of money of two or more partners are invested for the same or fixed period of time. It is known as a simple partnership.

In case of simple partnership investment is done for fixed period of time, suppose if there are n partners namely R, S….n make investments of I1, I2……. In Rs respectively and the company makes a profit or loss, then the share of profit and loss of each partner can be calculated as:-

Share of R = I1 / (I1+ I2 …. +In) × P (or L).

Share of S = I2 / (I1+ I2 …. +In) × P (or L).

Share of n = In / (I1+ I2 …. +In) × P (or L).

**Compound partnership.**

If the investment of two or more partners is invested for a different period of time, the partnership is called compound or complex partnership.

In case of Compound or complex partnership investment is done for a varying periods of time, suppose if there are n partners R, S, T….n makes an investment of I1, I2, I3…….In for Time period T1, T2, T3….Tn respectively and company makes a profit or loss, then the share of profit and loss of each partner can be calculated as:-

Share of R = I1 ×T1/ (I1+ I2+I3 ….. +In) × P (or L).

Share of S = I2×T2 / (I1+ I2+I3 ….. +In) × P (or L).

Share of T = I2×T3 / (I1+ I2+I3 ….. +In) × P (or L).

Share of n = In ×Tn / (I1+ I2+I3 …. +In) × P (or L).

**The ratio of Division of Gains.**

- When investments of all the partners are for the same time, the profit or loss is distributed among the partners in the ratio of their investments.

Suppose M and N invest, p Rs and q Rs respectively for one year in a business, then at the end of the year.

(M’s share of profit): (N’s share of profit) = p: q.

- If their investments are for different time periods, then equivalent capitals are calculated for a unit of time. Now profit or loss is divided in the ratio of these capitals.

Suppose M invests Rs. p for x months and N invests Rs. q for y months then,

(M’s share of profit): (N’s share of profit) = px: qy.

**III.** If there are n partners who invest I1, I2, I3….In amounts for T1:T2:T3…Tn time period then profit sharing or loss sharing ratio can be calculated as :-

I1×T1: I2×T2: I3×T3…..InTn= P1: P2: P3….Pn. (where, P1, P2, P3…… Pn are profit).

- If there are n partners who invested I1, I2, I3….In and the ratio of their profit P1: P2: P3….Pn. Then the ratio of their time period i.e. T1:T2:T3…Tn is given by:-

T1:T2:T3… Tn = P1/I1: P2/I2: P3/I3…. Pn/In

**Note:- **

In question-related to partnership it is crucial to determine the ratio in which profit or loss must be shared among the partners, once the ratio is find other values like share of each partner, time of investment, Amount of investment etc. can be calculated.

**Example: –** P and Q starts a business by investing 30000 Rs and 90000 Rs respectively. Find the ratio of their profit for one year?

**Explanation: –** By using formula

= I1×T1: I2×T2 (where, I1, I2 are an investment, T1, T2 are time period)

= 30000×12: 90000×12

= 3: 9

= 1:3

Hence, the ratio of their profit is 1:3.

**Example: –** A start a business with 4000 Rs and B joins the business 5 month later with 9000 Rs. Find the share of A and B if the total profit is 37,000 Rs after one year?

**Explanation:-**

Let us suppose the ratio of their investments be A: B

= A : B

= 4000×12: 9000×7

= 48 : 63

= 16 : 21

A’s share = 16/ (16+21) × 37000 = 16/ 37 × 37000 = 16000 Rs.

B’s share = 21/ (16+21) × 37000 = 21/37× 37000 = 21000 Rs.

**Example: –** Anita, Mohan and Riya opened a sweet shop in partnership by investing 32000 Rs, 20000Rs and 12000Rs respectively. After 2 years, they had a profit of 80000.what was the share of Riya in the profit?

**Explanation:- **

Let us suppose the ratio of investments of Anita, Mohan and Riya be A: M: R

A: M: R = I1×T1: I2×T2: I3×T3 (By using formula)

= 32000×24: 20000×24: 12000×24 (2 year = 24 month)

= 32: 20: 12.

= 16: 10: 6 (Dividing by 2)

= 8: 5:3

Hence, A: M: R = 8:5:3

Riya’s share = 3/ (8+5+3) × 80000

= 3/16 × 80000

= 3×5000

=15000 Rs.

**Example: –** Rohan, Sita and Tina invest in a project in the ratio of 2:3:4, if their profit sharing ratio is 3: 4: 5. Then calculate the ratio of their time period for which they invested?

**Explanation:-**

By using formula

T1:T2:T3… Tn = P1: P2: P3…. Pn

I1 I2 I3 In

P1: P2: P3 = 3:4:5

I1: I2: I3 = 2:3:4

= 3: 4: 5

2 3 4

= 3 × 12: 4 × 12: 5 × 12

2 3 4

= 3×6: 4×4: 5×3 = 18:16:15.

Hence, the ratio of their time period is R: S: T = 18:16:15.

**Example: – **A and B opened a company into partnership, B’s investment is equal to one-fifth of A’s investment. Out of the total profit of Rs 15420 at the end one year, what is B’s share?

**Explanation:-**

Let the investment of A be x

B’s investment = 1/5 x

Ratio of the investment of A: B = x: 1/5x

= 5:1

Therefore, the share of B’s in the profit = 1/ (5+1) ×15420

= 1/6 ×15420

=2570 Rs.

**Example: –** Deepak started a travel agency with Rs 5500 and later it was joined by his brother Amit with Rs 6000, at the end of one year profit is divided between them equally. For how many months Amit joined the travel agency?

**Explanation:-**

Let Amit joined the travel agency for x months

It is given in the question that profit is divided equally.

Therefore the ratio of profit = 1:1

Ratio of their investments = Ratio of their Profit.

(5500×12): (6000× x) = 1:1

5500×12 = 1

6000× x 1

= 11 = 1

x 1

= x = 11 months.

Hence, Amit invests for 11 months.

**Example: – **P and Q invest in a business in the ratio of 2:3. If 10 % of the total profit goes to charity, if Q share in the profit is 2700Rs, then the total profit?

**Explanation:-**

Let, the investment of P and Q in the business be 2x and 3x respectively.

Total profit = y

Profit distributed between P and Q = 90 /100 × y = 9/10 y

Q share in the profit = 3/5×9/10 y = 2700

= y = 2700×10×5

9×3

= y = 5000 Rs.

Hence, the total profit is 5000 Rs.

**Example:-**If five times of A’s capital( investment) is equal to five times of B’s capital, which is equal to 10 times of C’s capital, then out of the total profit 35652Rs, How much amount will B gets?

**Explanation: –** Given: 5A’s = 5 B’s= 10 c’s

By comparing 5A’s =5 B’s

A/B = 5/5

A: B = 1:1……… (i)

By comparing 5 B’s = 10 c’s

B/C = 10/5

B: C = 2:1………..(ii)

By solving (i) and (ii)

A: B = 1 : 1

B: C = 2 : 1

A: B: C = 2: 2:1

B’s Share = 2/(2+2+1) × 35625

= 2/5 × 35625

=2 ×7125

= 14250 Rs.

Hence, B will get 14250 Rs.

**Example: –** X, Y, and Z invested 22000 in a business, X invested Rs 5000 more than Y and Y invested Rs 2000 less than Z, out of the total profit of Rs 44000 find Y share?

**Explanation:- **

Given = X+Y+Z = 22000 Rs ………. (i)

Let the amount invested by Z = M Rs

Amount invested by Y = (M – 2000) Rs

Amount invested by X = (M – 2000 +5000) = (M+3000) Rs

By substituting the value of X, Y, Z in equation (i)

X+Y+Z = 22000

M+3000+ M – 2000+M = 22000

3M +1000 = 22000

3M = 22000 – 1000

M = 21000/3

M = 7000 Rs

Therefore,

M= Z = 7000 Rs

Y = (M – 2000) = (7000 – 2000) = 5000 Rs

X = (M+3000) = (7000 + 3000) = 10000 Rs

Therefore, the ratio of X: Y: Z = 10000: 5000:7000

= 10:5:7

Therefore, Y share = 5/ (10+5+7) × 44000

= 5/22 × 44000

= 5 × 2000

= 10,000 Rs.

**Example: –** Renu started the business of cloth with Rs 5500. After 4 months Anil joins Renu as its partner. After one year the profits are divided between them in the ratio of 5:3. How much amount Anil contribute to the business?

**Explanation:-**

Let us suppose that Anil contribute Rs x

The ratio of their investments = Ratio of their Profit.

I1×T1: I2×T2 = P1:P2

Renu: Anil = 5500×12: x × 8 = 5:3

5500×12 = 5

x× 8 3

(By cross multiplying)

x = 5500×12×3

8×5

x = 550×3×3

x = 4950

Hence, Anil contribute in Business 4950 Rs.

#### Author :

Namrata Prasad

Designation: Banking Trainer

Sevementor Pvt Ltd

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