Quantitative Aptitude / Arithmetic

Partnership

Partnership: concepts, worked examples and practice.

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Start with the basics

Partnership, explained simply

Partners share profit using their agreed rule. If profit follows investment, compare both the money invested and the time it stays invested.

Try a small example

Asha invests ₹200 for 6 months. Ravi invests ₹300 for 4 months. Compare their contributions.

Show the steps

Asha: 200 × 6 = 1200 rupee-months.
Ravi: 300 × 4 = 1200 rupee-months.
Their contributions are equal, giving a 1:1 ratio under this rule.

Remember: Equal money alone does not mean equal contribution when the investment periods differ.

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Exam focus

MAT: Mathematical Skills

Prioritise common arithmetic, number properties and algebra. Label units before applying formulas.

CAT: Quantitative Aptitude

Start with arithmetic and algebra. Check domain restrictions and use estimation before long calculations; specialised topics are supporting preparation.

CMAT: Quantitative Techniques and Data Interpretation

Build reliable arithmetic and chart reading first. Keep speed proportional to certainty and verify the base of percentage changes.

NMAT: Quantitative Skills

Budget time within the section. In data sufficiency, separate the two statements before combining them.

XAT: Quantitative Aptitude and Data Interpretation

Combine common quantitative skills with accurate interpretation of unfamiliar data. Recheck units and assumptions.

SNAP: Quantitative, Data Interpretation and Data Sufficiency

Choose a fast method only after identifying the base and units. In sufficiency questions, test uniqueness rather than calculating unnecessarily.

Check your understanding

Explain the idea in your own words before opening the answer. Then apply it to the example.

Capital and Time

Explain the main rule in capital and time, then apply it to a small example. State the assumption that makes your reasoning valid.

Review the note

Check your answer

When profit is shared in proportion to investment, use capital multiplied by the time for which it was invested. This is a model, not a universal legal rule for partnerships.

Worked example: A invests 6000 for 12 months and B invests 9000 for 8 months. Their capital-time products are both 72000, so they split a 10000 profit equally under this rule.

Changing Investments

Explain the main rule in changing investments, then apply it to a small example. State the assumption that makes your reasoning valid.

Review the note

Check your answer

Split a changing investment into periods. Add capital-time products for each partner before simplifying the ratio.

Worked example: A invests 4000 for 6 months then 8000 for 6 months: 24000+48000=72000. B invests 6000 for 12 months: also 72000. Their effective contributions are equal.

Practice questions

Bharatiya Pathshala

Opening preparation notes...

BEGINNER

Partnership: visual worked lesson

Core idea

Partners share profit using their agreed rule. If profit follows investment, compare both the money invested and the time it stays invested.

Solving method

Build one capital-by-time row for each partner and each change. Add each partner's contributions, then divide profit in that ratio.

Worked example

Asha invests ₹200 for 6 months. Ravi invests ₹300 for 4 months. Compare their contributions. 1. Asha: 200 × 6 = 1200 rupee-months. 2. Ravi: 300 × 4 = 1200 rupee-months. 3. Their contributions are equal, giving a 1:1 ratio under this rule.

Read the diagram

The last column uses both capital and time. Asha’s 200 × 6 and Ravi’s 300 × 4 are equal, so this stated sharing rule gives equal shares. If a partner changes their investment, compute capital × months separately for each interval. A different agreement may specify a different profit-sharing rule.

Exam-style application

A invests 12000 for 4 months, then 18000 for 8. B invests 16000 for the full year. A contributes 48000+144000=192000 capital-months; B contributes 192000. With profit 50000 and an agreed fixed salary of 10000 for A before sharing, residual profit is 40000. Each gets 20000 of that; A receives 30000 overall and B 20000.

Common mistakes

Equal money alone does not mean equal contribution when the investment periods differ. A salary or commission specified before profit sharing must be handled first. Capital-time sharing is used only when the problem states that rule.

Compare capital multiplied by investment time. Under capital × time sharing: 1200 : 1200 = 1 : 1. — Compare capital multiplied by investment time

Under capital × time sharing: 1200 : 1200 = 1 : 1. — Compare capital multiplied by investment time

Formulas to remember

Time-weighted capital = sum of capital × months

Profit ratio follows the agreed sharing rule

Source record: Bharatiya Pathshala — original illustrated lessons.

Partnership, explained simply

Try a small example

MAT: Mathematical Skills

CAT: Quantitative Aptitude

CMAT: Quantitative Techniques and Data Interpretation

NMAT: Quantitative Skills

XAT: Quantitative Aptitude and Data Interpretation

SNAP: Quantitative, Data Interpretation and Data Sufficiency

Check your understanding

Capital and Time

Changing Investments

Partnership, explained simply

Try a small example

Partnership: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Capital and Time

Worked example

Changing Investments

Worked example

Application and strategy

Worked application

Common traps and strategy

Ratios and capital-time sharing

Core idea

Solving method

Worked example

Common mistakes

MAT: Mathematical Skills

CAT: Quantitative Aptitude

CMAT: Quantitative Techniques and Data Interpretation

NMAT: Quantitative Skills

XAT: Quantitative Aptitude and Data Interpretation

SNAP: Quantitative, Data Interpretation and Data Sufficiency

Check your understanding

Capital and Time

Changing Investments

Partnership: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Capital and Time

Worked example

Changing Investments

Worked example

Application and strategy

Worked application

Common traps and strategy

Ratios and capital-time sharing

Core idea

Solving method

Worked example

Common mistakes