Division as it relates to ratios and proportion — splitting quantities in given ratios.
## Core concept
Division in the context of ratio and proportion means partitioning a total quantity into parts that maintain a specified ratio. This is not arithmetic division, but rather proportional allocation.
When you divide a quantity *Q* in the ratio *a : b : c*, you split *Q* into three parts such that: - Part 1 : Part 2 : Part 3 = a : b : c - Part 1 + Part 2 + Part 3 = Q
The key principle: if the ratio is *a : b : c*, then the total parts = *a + b + c*, and each share is proportional to its ratio component.
## Formula / rule
To divide Q in ratio a : b : c:
- Sum of ratio parts = *a + b + c*
- Part 1 = (a / (a + b + c)) × Q
- Part 2 = (b / (a + b + c)) × Q
- Part 3 = (c / (a + b + c)) × Q
Verification: Sum of all parts must equal Q.
This extends to any number of parts (2, 4, 5, etc.).
## Common exam applications
Profit/Loss sharing among partners - Profits are divided among partners in their capital contribution ratio. - E.g., if A, B, C invest in ratio 2:3:5, profit is divided in the same ratio.
Resource allocation - Dividing overhead costs, materials, or time in a given ratio.
Inheritance/property division - Assets split among beneficiaries in specified ratios.
Mixture problems - Combining substances in given ratios and then dividing the mixture.
## Worked example
Question: A sum of ₹12,000 is to be divided among Arun, Bhav, and Chitra in the ratio 2 : 3 : 5. How much does each receive?
Solution: - Ratio = 2 : 3 : 5 - Sum of ratio parts = 2 + 3 + 5 = 10 - Arun's share = (2/10) × 12,000 = ₹2,400 - Bhav's share = (3/10) × 12,000 = ₹3,600 - Chitra's share = (5/10) × 12,000 = ₹6,000
Verification: 2,400 + 3,600 + 6,000 = 12,000 ✓
## Common mistakes
- Confusing ratio parts with actual amounts. The ratio 2:3:5 does *not* mean ₹2, ₹3, ₹5 — it means proportional shares.
- Forgetting to add all ratio components. Always sum *a + b + c* before calculating each share.
- Not verifying the answer. Always add back all parts to confirm they total the original quantity.
- Misapplying to non-ratio contexts. Division in ratio is *only* for proportional sharing, not simple arithmetic division.
- Arithmetic errors in multiplication/division. Ensure fractions are reduced before multiplying by the total.
## Exam tip
In CA Foundation, division questions are typically straightforward once you identify the ratio and total quantity. Draw a clear working showing: 1. The ratio and its sum. 2. Each fraction applied to the total. 3. Final verification.
Examiners reward clean presentation and verification as much as correctness.