Partnership Questions for UP POLICE CONSTABLE

Basic Partnership Concept

A partnership is when two or more people invest money in a business and share profits/losses. The key rule: profit or loss is divided in the ratio of their investments (capital) and the time they kept that capital invested. Think of it like a restaurant — if A puts in 50,000 rupees for 12 months and B puts in 30,000 for 12 months, A gets more profit because A invested more. The ratio of their profit share is 50,000 : 30,000 = 5 : 3.

• Profit ratio = (Capital × Time) ratio for each partner
• If time period is same for all, profit ratio = capital ratio only
• If capital is same, profit ratio = time ratio only
• Always reduce ratios to simplest form before dividing profit
• Total profit = sum of all individual profits

When Capital and Time Both Vary

This is the most common exam scenario. Each partner's share depends on both how much they invested AND for how long. You multiply capital by time for each partner, then set up a ratio. For example: A invests 40,000 for 8 months, B invests 50,000 for 10 months. A's contribution = 40,000 × 8 = 320,000. B's contribution = 50,000 × 10 = 500,000. Profit ratio = 320,000 : 500,000 = 32 : 50 = 16 : 25. If total profit is 4,100, A gets (16/41) × 4,100 = 1,600 and B gets (25/41) × 4,100 = 2,500.

• Multiply each partner's capital by their time period
• These products form the profit-sharing ratio
• Divide total profit using this ratio
• Watch for capital changes mid-year — add separately
• Always check: sum of individual profits = total profit

Capital Changes During Year

Sometimes a partner adds or withdraws money mid-year. You must calculate their contribution in two parts: first amount for first period, second amount for second period. For instance, if A invests 50,000 for 6 months, then adds 30,000 more for the remaining 6 months, A's total contribution = (50,000 × 6) + (30,000 × 6) = 300,000 + 180,000 = 480,000. This is a common exam trap — aspirants forget to split the time period.

• When capital changes, split the year into periods
• Calculate contribution for each period separately
• Add all contributions for that partner
• Then use the standard profit-sharing formula
• Watch for withdrawals — they reduce contribution

Working Partner & Salary

In some partnerships, one partner actively manages the business and gets a salary in addition to profit share. The salary is paid first from profit, then the remaining profit is divided based on capital and time. For example, if total profit is 10,000 and working partner gets 2,000 salary, remaining 8,000 is divided by the profit ratio. This is less common in UP Police but appears occasionally.

• Working partner salary is deducted from total profit first
• Remaining profit is then divided by capital-time ratio
• Salary is a fixed amount, not part of profit-sharing ratio
• Always clarify: is salary given or to be calculated?

• Forgetting to multiply capital by time — using capital ratio alone when time differs. If A invests 100,000 for 6 months and B invests 100,000 for 12 months, profit ratio is NOT 1:1, it's 6:12 = 1:2.
• Not reducing ratios to simplest form before dividing profit. This causes calculation errors and wastes time. Always simplify 320,000 : 500,000 to 16 : 25 first.
• Mishandling mid-year capital changes. Aspirants often use only the final capital amount, ignoring the time-weighted calculation. Split the year properly.
• Confusing withdrawal with reduction. If A withdraws 10,000, the remaining capital is (original - 10,000), not 10,000 itself.
• Adding up individual profits incorrectly. Always verify: sum of all shares = total profit. If it doesn't match, you made an arithmetic error.

• C × T = Contribution. Think 'Capital Times Time gives contribution.' This is the foundation of every partnership problem.
• Ratio first, divide second. Always set up the ratio (C×T for each partner) BEFORE dividing the profit. This prevents mixing up numerators.
• Split the year. If capital changes mid-year, split into two periods. Use a timeline if needed — it saves errors.
• Check your answer. Sum of individual profits must equal total profit. If not, backtrack immediately.

• UP Police partnership questions are straightforward — no hidden tricks, just arithmetic. Focus on speed and accuracy, not complex logic.
• Most questions have capital and time both varying. Practice this scenario the most. Single-variable (capital only or time only) is rare.
• Ratio simplification is critical. Examiners often give numbers that simplify nicely (e.g., 320,000 : 500,000 = 16 : 25). Use this to check your work.
• Time is usually in months. Watch for questions mixing months and years — convert everything to months first to avoid errors.
• Expect 1-2 questions per paper, each worth 1-2 marks. They appear in the 20-25 minute window of the Numerical section. Practice solving in under 2 minutes per question.