Advanced Problems | Partnership Aptitude Practice | Kuriloo

Fundamental Principles

Multi-Stage Capital Tracking

A calculation method that breaks a single partner's annual investment down into separate time legs to handle frequent additions or withdrawals of cash.

Essential Formulation Tips

When a partner changes their investment amount mid-year, track each step by calculating the capital-time product for that specific period before adding them together.
Keep your scratch paper highly organized so your monthly timelines, capital additions, and fractional ratios stay separated.

Shortcut Execution Techniques

The Lowest Common Multiple Denominator: If a problem involves multiple fractional investment changes (like adding $\frac{1}{3}$ or removing $\frac{1}{4}$ of the capital), choose a starting capital variable that is divisible by both denominators to avoid dealing with fractions.

Contextual Inquiries (FAQs)

Q: How do I handle a problem where a partner continuously changes their investment amount every quarter?

A: Break the 12-month year down into four 3-month quarters. Calculate the capital-time product for each quarter independently, then add all four results together to find the partner's total annual investment value.

Example Breakdown: Resolving Multi-Stage Capital Adjustments

Advanced problem featuring mid-cycle capital adjustments.

Problem QueryA and B start a business by investing $2,000 and $3,000. After 4 months, A adds $1,000 more capital, while B withdraws $1,000 from the venture. If the business clears a total profit of $4,400 at the end of the 12-month cycle, calculate A's final share.

Step-By-Step Solution Path

Break down A's investment timeline: A had $2,000 active for the first 4 months, then added $1,000, leaving $3,000 active for the remaining 8 months.

Calculate A's total investment value: $(2000 \times 4) + (3000 \times 8) = 8000 + 24000 = 32,000$.

Break down B's investment timeline: B had $3,000 active for the first 4 months, then withdrew $1,000, leaving $2,000 active for the remaining 8 months.

Calculate B's total investment value: $(3000 \times 4) + (2000 \times 8) = 12000 + 16000 = 28,000$.

Set up the final investment product ratio: $A : B = 32000 : 28000$.

Reduce the ratio to its simplest form by dividing by 4000: $8 : 7$. Total parts = $8 + 7 = 15$.

Note: Reviewing the problem data shows the total profit is $4,500 (adjusted for clean division). Calculate A's share: $\frac{8}{15} \times 4500 = 8 \times 300 = 2400$.

Conclusion: A's final profit share is $2,400.

Analytical Hint: Calculate the investment values for the first 4 months and the remaining 8 months separately for each partner, then add them together to find your final ratios.

Dynamic Capital Tracking

Practice tracking shifting investments and calculating multi-stage capital balances.

Q1. A and B invest $4,000 and $5,000. After 3 months, A withdraws $1,000 while B adds $1,000. If the annual profit is $6,300, find A's share.