Updated profit-sharing ratio after increasing investments: Aarti, Vinita, and Kamla invest in the ratio 5 : 7 : 6 initially. Next year they increase investments by 26%, 20%, and 15% respectively. Find the ratio in which the second-year profit should be distributed.

Introduction / Context:
Profit in a year is proportional to the invested capital for that year. When investments change by given percentages, multiply each base part by (1 + percentage change) to get the effective parts for that year, then reduce to a clean ratio for distribution.

Given Data / Assumptions:

• Initial ratio: 5 : 7 : 6.
• Increases: Aarti +26%, Vinita +20%, Kamla +15%.
• Second-year profit ∝ updated capitals.

Concept / Approach:
Multiply each initial part by the growth factor: 1.26, 1.20, 1.15 respectively, then convert to integers by scaling (e.g., multiply by 10) and simplify if possible.

Step-by-Step Solution:

Verification / Alternative check:
Any common multiplier applied to 21 : 28 : 23 corresponds to the same proportional distribution; thus this ratio uniquely represents the second-year split.

Why Other Options Are Wrong:
Other options do not preserve the precise 1.26, 1.20, and 1.15 factors applied to 5 : 7 : 6.

Common Pitfalls:
Adding percentage points directly to the ratio numbers instead of multiplying by growth factors; failing to simplify properly.

Final Answer:
21 : 28 : 23