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Partnership

Practice MCQs

Partnerships are business arrangements where two or more individuals or entities join together to share profits, losses, and responsibilities in a mutually agreed-upon manner. Partnerships offer the advantages of shared resources, expertise, and risk, allowing for collaborative decision-making and the potential for growth and success in various industries and sectors.

Quantitative Aptitude Partnership Competitive Exams

Partnership is an important quantitative aptitude topic based on sharing profit or loss among partners according to their investment and time period. These questions are commonly asked in banking exams, government exams, aptitude tests, and business mathematics.

What is Partnership?

A partnership is a business arrangement where two or more persons invest money in a business and agree to share the profit or loss. The persons involved are called partners.

In aptitude questions, profit is usually divided in the ratio of capital invested and time period. If all partners invest for the same time, profit is divided only according to their capital.

Quick idea: Partnership profit sharing is based on Capital × Time.
Term Meaning Example
Capital Money invested by a partner ₹50,000 invested by A
Time Duration for which capital remains invested 8 months, 1 year
Profit Gain from business after expenses Total profit = ₹24,000
Loss Business loss shared by partners Total loss = ₹12,000
Working Partner Partner who actively manages the business Gets salary or commission first
Sleeping Partner Partner who only invests capital Shares profit based on investment

“In partnership, profit follows the money and the time for which it was used.”

Aptitude Tip
Key points
  • If time is same, divide profit in capital ratio.
  • If time is different, divide profit in capital × time ratio.
  • Salary or commission is deducted before profit sharing.
  • Loss is also divided in the same ratio as profit.
  • Use months consistently when time periods differ.
  • Do not ignore partners who join or leave midway.
capital time profit ratio

Visual Understanding

These diagrams show how partnership profit is divided according to investment and time.

Simple Partnership
Partner A ₹40,000 Partner B ₹60,000 Profit Ratio 40 : 60 = 2 : 3 Same time period, so ratio depends only on capital.
\[ \text{Profit Ratio} = C_A:C_B \]

When both partners invest for the same time, divide profit according to capital.

Capital × Time Method
A ₹30,000 × 12 B ₹40,000 × 9 A's Product 360000 B's Product 360000 Profit Ratio = 1 : 1
\[ \text{Profit Ratio} = C_A T_A : C_B T_B \]

When time periods differ, multiply each partner’s capital by time.

Important Formulas and Rules

Same Time Period
\[ \text{Profit Ratio} = C_A:C_B \]

Use when partners invest for the same duration.

Different Time Period
\[ \text{Profit Ratio} = C_A T_A:C_B T_B \]

Use capital multiplied by time.

Share of Profit
\[ \text{Share} = \frac{\text{Partner Ratio}}{\text{Total Ratio}}\times \text{Total Profit} \]

Use after finding the correct ratio.

Net Profit After Salary
\[ \text{Net Profit} = \text{Total Profit} - \text{Salary or Commission} \]

Salary or commission is deducted before sharing remaining profit.

Rule: Profit or loss is divided in the ratio of \(\text{Capital} \times \text{Time}\), unless the question gives a special condition.

Common Types of Partnership Questions

Simple Partnership

Partners invest for the same time period.

  • Only capital ratio
  • Easy profit sharing
  • Same duration
  • Direct ratio
Compound Partnership

Partners invest for different time periods.

  • Capital × Time
  • Partner joins later
  • Partner leaves early
  • Time is important
Working Partner

One partner receives salary or commission.

  • Deduct salary first
  • Share remaining profit
  • May get fixed amount
  • May also share profit
Unknown Investment

One partner’s capital or time is unknown.

  • Use profit ratio
  • Form equation
  • Capital may be unknown
  • Time may be unknown
Exam approach: First decide whether the time period is same or different. Then form the investment-time ratio.
Method Bank
Same Time

A invests ₹40,000 and B invests ₹60,000.

\[ A:B = 40000:60000 = 2:3 \]
Different Time

A invests ₹20,000 for 12 months, B invests ₹30,000 for 8 months.

\[ A:B = 20000\times12 : 30000\times8 \]
Share from Ratio

If ratio is \(2:3\), total profit is ₹10,000.

\[ A = \frac{2}{5}\times10000 \]
After Salary

Salary is removed before profit sharing.

\[ \text{Remaining Profit} = P - S \]

Tip: Convert years into months if another partner’s time is already given in months.

Partner Joining Timeline
Start End A invests for 12 months B invests for 8 months B joins later Different time periods must be considered
When a partner joins late or leaves early, use only the actual investment period.

Step-by-Step Solving Method

Step Action Example
Step 1 Identify each partner’s capital. A = ₹40,000, B = ₹60,000
Step 2 Identify the investment period. Both invested for 1 year.
Step 3 Form the ratio. \(40000:60000 = 2:3\)
Step 4 Find total ratio parts. \(2+3=5\)
Step 5 Divide total profit according to ratio. If profit is ₹25,000, A gets \(\frac{2}{5}\times25000\).
Important: If the question includes salary, commission, or bonus for a working partner, deduct it before dividing the remaining profit.

Solved Examples

Question Method Answer
A invests ₹40,000 and B invests ₹60,000 for the same time. If total profit is ₹25,000, find their shares.
\[ A:B = 40000:60000 = 2:3 \]
\[ A = \frac{2}{5}\times25000 = 10000 \]
\[ B = \frac{3}{5}\times25000 = 15000 \]
A = ₹10,000, B = ₹15,000
A invests ₹30,000 for 12 months and B invests ₹40,000 for 9 months. Find the profit ratio.
\[ A:B = 30000\times12 : 40000\times9 \]
\[ A:B = 360000:360000 = 1:1 \]
1 : 1
A invests ₹50,000 and B invests ₹75,000. Total profit is ₹36,000. Find B's share.
\[ A:B = 50000:75000 = 2:3 \]
\[ B = \frac{3}{5}\times36000 = 21600 \]
₹21,600
A invests ₹20,000 for 12 months. B invests ₹30,000 for 8 months. Profit is ₹24,000. Find A's share.
\[ A:B = 20000\times12 : 30000\times8 \]
\[ A:B = 240000:240000 = 1:1 \]
\[ A = \frac{1}{2}\times24000 = 12000 \]
₹12,000
A and B invest in the ratio \(3:5\). Their total profit is ₹40,000. Find A's share.
\[ A = \frac{3}{3+5}\times40000 \]
\[ A = \frac{3}{8}\times40000 = 15000 \]
₹15,000
A invests ₹60,000 and B invests ₹40,000. B is a working partner and receives ₹5,000 salary from total profit ₹35,000. Divide the remaining profit. Salary is deducted first.
\[ \text{Remaining Profit} = 35000 - 5000 = 30000 \]
\[ A:B = 60000:40000 = 3:2 \]
\[ A = \frac{3}{5}\times30000 = 18000 \]
\[ B = 5000 + \frac{2}{5}\times30000 = 17000 \]
A = ₹18,000, B = ₹17,000
A invests ₹45,000 and B invests ₹60,000. If A's share in profit is ₹9,000, find total profit.
\[ A:B = 45000:60000 = 3:4 \]
A's 3 parts = ₹9,000.
\[ 1\text{ part} = 3000 \]
Total parts \(=7\).
\[ \text{Total Profit} = 7\times3000 = 21000 \]
₹21,000
A invests ₹24,000 for 10 months. B invests ₹30,000 for 8 months. Find the profit ratio.
\[ A:B = 24000\times10 : 30000\times8 \]
\[ A:B = 240000:240000 = 1:1 \]
1 : 1

Note: Always check whether a partner joined late, left early, or received salary/commission.

Common Traps and Shortcuts

Common Traps
  • Ignoring different investment periods.
  • Dividing profit only by capital when time is different.
  • Forgetting to deduct salary before sharing profit.
  • Adding working partner salary after dividing full profit.
  • Not converting years and months into the same unit.
  • Confusing capital ratio with profit share amount.
Useful Shortcuts
  • Same time: use only capital ratio.
  • Different time: use capital × time ratio.
  • Use months as common time unit.
  • Salary is deducted before profit sharing.
  • Loss is divided in the same ratio as profit.
  • If one share is given, find value of one ratio part.
Exam approach: Write each partner’s capital and time in a table before forming the profit-sharing ratio.

Practice

A) Multiple Choice Questions
  1. A invests ₹20,000 and B invests ₹30,000 for the same time. Find their profit ratio.
    1 : 2 2 : 3 3 : 2 4 : 5
  2. A and B invest in the ratio \(3:4\). Total profit is ₹28,000. Find A's share.
    ₹10,000 ₹12,000 ₹16,000 ₹18,000
  3. A invests ₹40,000 for 12 months and B invests ₹60,000 for 8 months. Find profit ratio.
    1 : 1 2 : 3 3 : 2 4 : 3
  4. A and B share profit in ratio \(5:3\). If total profit is ₹40,000, B gets:
    ₹12,000 ₹15,000 ₹20,000 ₹25,000
  5. If total profit is ₹50,000 and working partner salary is ₹10,000, remaining profit to be shared is:
    ₹30,000 ₹35,000 ₹40,000 ₹50,000
B) Solve the Higher-Order Problems
  1. A invests ₹50,000 and B invests ₹75,000 for the same time. Total profit is ₹30,000. Find both shares. (Hint: Use capital ratio.)
  2. A invests ₹30,000 for 12 months and B invests ₹45,000 for 8 months. Find the profit ratio. (Hint: Use capital × time.)
  3. A and B invest in the ratio \(4:5\). If B's profit share is ₹25,000, find total profit. (Hint: Find value of one part.)
  4. A invests ₹60,000 and B invests ₹40,000. B gets ₹6,000 as salary from total profit ₹46,000. Divide the profit. (Hint: Deduct salary first.)
  5. A invests ₹25,000 for 10 months. B invests ₹20,000 for 12 months. If total profit is ₹49,000, find A's share. (Hint: Compare \(25000\times10\) and \(20000\times12\).)
C) Match the Concept with the Correct Meaning
Concept Correct Meaning
Capital Money invested by a partner
Simple Partnership Partners invest for same time period
Compound Partnership Partners invest for different time periods
Working Partner Partner who manages business and may receive salary
Sleeping Partner Partner who invests but does not actively manage
Profit Ratio Ratio in which profit is shared
Aptitude Reminder

Partnership questions are solved by comparing each partner’s investment contribution. If time periods are different, contribution means capital multiplied by time. After finding the ratio, divide profit or loss according to the ratio.

Task: Create five partnership questions using simple partnership, compound partnership, working partner salary, unknown total profit, and unknown share.

Show Suggested Answers
Multiple Choice
  1. 2 : 3
    \[ A:B = 20000:30000 = 2:3 \]
  2. ₹12,000
    Total ratio parts \(=3+4=7\).
    \[ A = \frac{3}{7}\times28000 = 12000 \]
  3. 1 : 1
    \[ A:B = 40000\times12 : 60000\times8 \]
    \[ A:B = 480000:480000 = 1:1 \]
  4. ₹15,000
    Total ratio parts \(=5+3=8\).
    \[ B = \frac{3}{8}\times40000 = 15000 \]
  5. ₹40,000
    \[ \text{Remaining Profit} = 50000 - 10000 = 40000 \]
Higher-Order Problems
  1. A invests ₹50,000 and B invests ₹75,000:
    \[ A:B = 50000:75000 = 2:3 \]
    Total profit \(= ₹30,000\).
    \[ A = \frac{2}{5}\times30000 = 12000 \]
    \[ B = \frac{3}{5}\times30000 = 18000 \]
    Answer = A = ₹12,000, B = ₹18,000.
  2. A invests ₹30,000 for 12 months, B invests ₹45,000 for 8 months:
    \[ A:B = 30000\times12 : 45000\times8 \]
    \[ A:B = 360000:360000 = 1:1 \]
    Answer = 1 : 1.
  3. A : B \(=4:5\), B's share \(= ₹25,000\).
    \[ 5\text{ parts} = 25000 \]
    \[ 1\text{ part} = 5000 \]
    Total parts \(=9\).
    \[ \text{Total Profit} = 9\times5000 = 45000 \]
    Answer = ₹45,000.
  4. Total profit \(= ₹46,000\), B's salary \(= ₹6,000\).
    \[ \text{Remaining Profit} = 46000 - 6000 = 40000 \]
    Investment ratio:
    \[ A:B = 60000:40000 = 3:2 \]
    \[ A = \frac{3}{5}\times40000 = 24000 \]
    \[ B = 6000 + \frac{2}{5}\times40000 = 22000 \]
    Answer = A = ₹24,000, B = ₹22,000.
  5. A invests ₹25,000 for 10 months, B invests ₹20,000 for 12 months:
    \[ A:B = 25000\times10 : 20000\times12 \]
    \[ A:B = 250000:240000 = 25:24 \]
    Total profit \(= ₹49,000\), total parts \(=49\).
    \[ A = \frac{25}{49}\times49000 = 25000 \]
    Answer = ₹25,000.
Concept Matching
  1. Capital → Money invested by a partner
  2. Simple Partnership → Partners invest for same time period
  3. Compound Partnership → Partners invest for different time periods
  4. Working Partner → Partner who manages business and may receive salary
  5. Sleeping Partner → Partner who invests but does not actively manage
  6. Profit Ratio → Ratio in which profit is shared
Clue Explanation

Partnership profit sharing is based on contribution. Contribution means capital alone when time is same, and capital multiplied by time when time is different.

Exam tips
  • Always write capital and time separately.
  • Use capital ratio only when time is same.
  • Use capital × time when time differs.
  • Deduct working partner salary before sharing remaining profit.
  • Convert years and months into one common unit.
  • Loss is shared in the same ratio as profit.
Practice MCQs