Investment Ratio | Partnership Aptitude Practice | Kuriloo

Fundamental Principles

Capital Factor Isolation

An algebraic rearrangement of the core partnership balance used to find missing dimensions, written as: $\text{Investment Ratio} = \frac{\text{Profit Share}}{\text{Time Duration}}$.

Essential Formulation Tips

Use a clear algebraic variable (like $x$) to represent the unknown investment value in your initial layout.
Double-check that all fractional steps are completely cleared before running large multiplications.

Shortcut Execution Techniques

The Ratio Equivalence Shortcut: Instead of using large cash values, scale investment sums down into simplified ratio units during intermediate algebra steps to keep your scratchpad math clean.

Contextual Inquiries (FAQs)

Q: What should I do if a problem contains two unknown investment values?

A: Look for a secondary clue, such as a statement linking their investments (e.g., 'A invested $500 more than B'), to build a single-variable equation.

Example Breakdown: Isolating Capital from Time-Profit Constraints

Standard algebraic capital isolation challenge.

Problem QueryA and B enter into a business layout. A invests capital for 8 months. B invests for 6 months. At the end of the cycle, the profits are split in the ratio 4:3. If A's initial investment was $2,000, find B's capital input.

Step-By-Step Solution Path

Let B's unknown capital investment be represented by $x$.

Set up the product ratio for both partners: $(\text{Investment}_A \times \text{Time}_A) : (\text{Investment}_B \times \text{Time}_B)$.

Substitute known values: $(2000 \times 8) : (x \times 6) = 16000 : 6x$.

Match the product ratio to the given profit split: $\frac{16000}{6x} = \frac{4}{3}$.

Cross-multiply to solve for your variable: $16000 \times 3 = 4 \times 6x \implies 48000 = 24x$.

Isolate the investment variable: $x = \frac{48000}{24} = 2000$.

Conclusion: B's capital input was exactly $2,000.

Analytical Hint: Set up a fractional balance matching the capital-time product directly to the profit ratio, then solve for the missing variable.

Capital Extraction Challenges

Practice working backward to isolate unknown capital inputs from time and profit constraints.

Q1. John and Mark share business profits in the ratio 2:3. John invested $4,000 for 9 months. If Mark invested his capital for 6 months, how much money did Mark invest?