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Microlesson · 5-min read

Repeated Distribution Method (Reciprocal)

# Repeated Distribution Method

Used when service departments render reciprocal services to each other (e.g., Stores helps Canteen, Canteen helps Stores).

## Procedure

1. Take one service department and distribute its total to all production and service departments in the given ratio.

2. Take the next service department (which now has an updated balance) and distribute it similarly.

3. Keep cycling through all service departments repeatedly.

4. Stop when the balance of any service department is less than ₹50 (or whatever immaterial cut-off is given). At that point, transfer the small balance only to production departments (rounded) to close out.

## Key Idea

Every service department keeps "giving back" cost to others until the iterations make the residual balance negligible.

## When to Use

  • Mutual/reciprocal services exist.
  • Question allows iterative arithmetic.
  • Useful when only two service departments and quick recursion is feasible.

Worked example

### Example 1

Example — Repeated Distribution (skeletal):

After primary distribution: P₁=80,000; P₂=70,000; S₁=30,000; S₂=20,000.

Apportionment ratios:

  • S₁ → P₁ : P₂ : S₂ = 4 : 3 : 3
  • S₂ → P₁ : P₂ : S₁ = 3 : 4 : 3
RoundP₁P₂S₁S₂
Opening80,00070,00030,00020,000
Distribute S₁ (30,000 in 4:3:3)+12,000+9,000(30,000)+9,000
Distribute S₂ (29,000 in 3:4:3)+8,700+11,600+8,700(29,000)
Distribute S₁ (8,700 in 4:3:3)+3,480+2,610(8,700)+2,610
Distribute S₂ (2,610 in 3:4:3)+783+1,044+783(2,610)
... continue until balance < 50

Finally totals of S₁ and S₂ become 0, all cost is in P₁ and P₂.

⚠️ Common exam mistakes

  • Continuing iterations longer than necessary — stop once the balance is immaterial (< ₹50).
  • Forgetting that the ratio for S₁'s distribution does NOT include S₁ itself (no self-apportionment).
  • Treating it like Step-Down — Repeated Distribution keeps cycling, Step-Down closes once.
Reference:
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