Shares and partnerships is a prominent subtopic of Quantitative Aptitude sections of any examination. The questions from this topic can be high scoring and hence should not be ignored. Today in this post, we will be discussing Shares and Partnerships questions: the concepts and tips.

Table of Contents

**What is Partnership?**

Partnership is a formal arrangement between two or more persons to manage and operate a business and share its profit. There can be two types of partners in a business:

**Sleeping Partner:**This partner has nothing to do with the business management and he/she provides different resources like land, money, etc.**Working Partner:**This partner manages the business (active partner) and he/she plays an important role in production, marketing, etc. Working partner gets an incentive for managing the business and the remaining profit is divided according to the investment.

**Simple Partnership:**

**Unequal investment and equal time period:** If 2 partners A and B invest unequal amounts for the same period of time, the ratio of their profits is given by

(Profit of A)/(Profit of B) = (Investment of A)/(Investment of B)

**Equal Investment and unequal time period:** If 2 partners A and B invest equal amounts for different time periods, the ratio of their profits is given by

(Profit of A)/(Profit of B) = (Investment period of A)/(Investment period of B)

**Practice questions of Quant topics by attempting the sectional tests here.**

**Compound Partnership**

**Unequal investment and unequal period of time:** If two partners invest unequal amounts for different time periods, the ratio of their profits is given by

(Profit of A)/(Profit of B) = (Investment of A * Investment period of A)/( Investment of B * Investment period of B)

**Attempt a FREE IBPS clerk mock test here.**

(I) If two partners A and B invest I_{A }and I_{B} respectively for equal period of time and they earn a total profit of P, then their profits P_{A }and P_{B} is given by

P_{A }**= **(I_{A }* P)/(I_{A} + I_{B}) and P_{B }**= **(I_{B }* P)/(I_{A} + I_{B})

(II)If two partners A and B invest I_{A }and I_{B} respectively for time period T_{A} and T_{B} and they earn a total profit of P, then their profits P_{A }and P_{B} is given by

P_{A }**= **(I_{A }* T_{A} * P)/{(I_{A }* T_{A}) + (I_{B }* T_{B})} and P_{B }**= **(I_{B }* T_{B} * P)/{(I_{A }* T_{A}) + (I_{B }* T_{B})}

**Attempt a FREE IBPS PO Mains mock test here.**

(III) If n partners are investing their money I_{1}, I_{2}, …, I_{n}for an equal period of time and their total profit is P, then their shares of profit are

P_{1 }**= **(I_{1 }* P)/(I_{1 }+ I_{2} + … + I_{n}), P_{2 }**= **(I_{2 }* P)/(I_{1 }+ I_{2} + … + I_{n}), …, P_{n }**= **(I_{n }* P)/(I_{1 }+ I_{2} + … + I_{n})

(IV) If n partners are investing their money I_{1}, I_{2}, …, I_{n}for time periods T_{1}, T_{2}, …, T_{n} and their total profit is P, then their shares of profit are

P_{1 }**= **(I_{1 }* T_{1} * P)/ {(I_{1 }* T_{1}) + (I_{2 }* T_{2}) + … + (I_{n }* T_{n})}, P_{2 }**= **(I_{2 }* T_{2} * P)/ {(I_{1 }* T_{1}) + (I_{2 }* T_{2}) + … + (I_{n }* T_{n})}, …, P_{n }**= **(I_{n }* T_{n} * P)/ {(I_{1 }* T_{1}) + (I_{2 }* T_{2}) + … + (I_{n }* T_{n})}

**Practice questions of Quant topics by attempting the sectional tests here.**

1. P, Q and R entered into a partnership and invested their amounts for time period in the ratio 2:3:5. The ratio of investments of P, Q and R was 5:10:3. If P’s share out of the profit was 14400, what was the profit?

a) Rs. 72,200

b) Rs. 76,800

c) Rs. 79,200

d) Rs. 74,400

e) Rs. 81,600

Answer key: c

Solution:

Profit will be distributed among P, Q and R in the ratio = (2 * 5) : (3 * 10) : (5 * 3) = 2:6:3

Sum of parts of ratio = 2 + 6 + 3

Value of profit = (11/2) * 14400 = Rs. 79,200

**Attempt a FREE SBI PO mock test here.**

2. Rakesh and Suresh invested Rs 30,000 and Rs 50,000 respectively to start a business and the ratio of the time for which Suresh and Rakesh invested is 3: 4. At the end of year Rakesh was paid Rs 18,000 as an incentive for managing the business and Suresh got a profit of Rs 40,000 from the remaining profit then what is the total profit obtained?

a) Rs. 72,000

b) Rs. 90,000

c) Rs. 75,000

d) Rs. 85,000

e) Rs. 60,000

Answer key: b

Solution:

Ratio of profit divided after incentive was paid = (30,000 * 4):(50,000 * 3) = 12: 15 = 4: 5

Remaining profit after the incentive was paid = Rs. 40,000 * (9/5) = Rs. 72,000

Total profit earned = Rs. 72,000 + Rs. 18,000 = Rs. 90,000

**Practice more such questions by attempting the sectional tests of Quant here.**

3. Prakash, Naresh and Vishal started a business in which their investments are in the ratio (1/40): (1/36): (1/45). At the end of 3 years Naresh withdraws 1/8^{th}of his initial investment after another year Prakash adds 1/6^{th} of his and after one more year Vishal adds 1/4^{th} of his initial investment. At the end of 7 years, then what is the respective ratio of profit amount received by them from the business?

a) 24: 25: 26

b) 13: 24: 15

c) 24: 25: 27

d) 27: 26: 24

e) Cannot be determined

Answer key: d

Solution:

Ratio of their investments = (1/40): (1/36): (1/45) = 9: 10: 8

Let the initial investment of Prakash, Naresh and Vishal be 900x, 1000x and 800x respectively

Ratio of their profit = (900x * 4 + 1050x * 3): (1000x * 3 + 875x * 4): (800x * 5 + 1000x * 2) = 6750: 6500: 6000 = 27: 26: 24

Practice more and more shares and partnerships questions to get acquainted with it. All the best for your examination!

**Study at your own convenience anywhere. Download the Oliveboard app now!**

Oliveboard is a learning & practice platform for premier entrance exams. We have helped over 1 crore users since 2012 with their Bank, SSC, Railways, Insurance, Teaching and other competitive Exams preparation.

** Oliveboard Live Courses & Mock Test Series**