Concept, Tips and Practice Questions for Shares and Partnerships

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.

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.

Shares and Partnerships questions: Types of partnership

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)

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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)

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Some important points to note while solving shares and partnerships questions

(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)}

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(III) If n partners are investing their money I₁, I₂, …, I_nfor an equal period of time and their total profit is P, then their shares of profit are

P₁ = (I₁ * P)/(I₁ + I₂ + … + I_n), P₂ = (I₂ * P)/(I₁ + I₂ + … + I_n), …, P_n = (I_n * P)/(I₁ + I₂ + … + I_n)

(IV) If n partners are investing their money I₁, I₂, …, I_nfor time periods T₁, T₂, …, T_n and their total profit is P, then their shares of profit are

P₁ = (I₁ * T₁ * P)/ {(I₁ * T₁) + (I₂ * T₂) + … + (I_n * T_n)}, P₂ = (I₂ * T₂ * P)/ {(I₁ * T₁) + (I₂ * T₂) + … + (I_n * T_n)}, …, P_n = (I_n * T_n * P)/ {(I₁ * T₁) + (I₂ * T₂) + … + (I_n * T_n)}

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

Shares and Partnerships Questions for Practice

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

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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

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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^thof 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!

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