A, B and C enter into a partnership. A initially invests ₹ 25 lakhs and adds another ₹ 10 lakhs after one year. B initially invests ₹ 35 lakhs and withdraws ₹ 10 lakhs after 2 years and C invests ₹ 30 lakhs. In what ratio should the profits be divided at the end of 3 years?

### Concept & Multi-Phase Investments To find the profit ratio, break down each partner's total time into distinct periods where their capital remains constant. Calculate the product of capital and time for each period, and sum them up. $$ \text{Equivalent Capital} = (\text{C}_1 \times \text{T}_1) + (\text{C}_2 \times \text{T}_2) + \dots $$ ### Step-by-Step Solution * **Given:** * Total business duration = $3 \text{ years}$ * **Calculate Equivalent Capital (in lakhs):** * **A:** Invests $25$ for $1 \text{ year}$, then adds $10$ (making it $35$) for the remaining $2 \text{ years}$. * A = $(25 \times 1) + (35 \times 2) = 25 + 70 = 95$ * **B:** Invests $35$ for $2 \text{ years}$, then withdraws $10$ (leaving $25$) for the remaining $1 \text{ year}$. * B = $(35 \times 2) + (25 \times 1) = 70 + 25 = 95$ * **C:** Invests $30$ for the full $3 \text{ years}$ without changes. * C = $(30 \times 3) = 90$ * **Calculate Profit Ratio:** * $\text{Ratio} = 95 : 95 : 90$ * Divide all terms by $5$: * $\text{Ratio} = 19 : 19 : 18$ * **Match Options:** * Option (c) is $20 : 19 : 18$, which is incorrect. * Since $19 : 19 : 18$ is not listed among (a), (b), or (c), the answer is "None of these". ### Exam Strategy & Shortcut Always keep the units in "lakhs" to avoid writing unnecessary zeros. Since all time intervals are exact years, use years directly instead of converting to months. This keeps calculations small and manageable. ### Common Pitfall Seeing a visually similar option like (c) $20 : 19 : 18$ and mistakenly selecting it under time pressure. Always trust your final derived ratio. ### Final Answer Therefore, the correct answer is **None of these**.