Q.A factory has two production departments, A and B, and one service department S. The following overheads are to be distributed among them:

Each overhead item is apportioned across all three departments on the basis suited to it — rent on floor area, depreciation on machine value, supervision on number of workers — and the columns are totalled.

Rent splits 1,500:1,000:500 (3:2:1), depreciation 50,000:40,000:10,000 (5:4:1), and supervision 30:20:10 (3:2:1); adding each department's shares gives its overhead.

Each item is apportioned on the basis appropriate to it.

Step 1 — Rent ₹3,000 on floor area (1,500 : 1,000 : 500 = 3 : 2 : 1, total 6 parts).

• A = 3,000 × 3/6 = ₹1,500
• B = 3,000 × 2/6 = ₹1,000
• S = 3,000 × 1/6 = ₹500

Step 2 — Depreciation ₹2,000 on machinery value (50,000 : 40,000 : 10,000 = 5 : 4 : 1, total 10 parts).

• A = 2,000 × 5/10 = ₹1,000
• B = 2,000 × 4/10 = ₹800
• S = 2,000 × 1/10 = ₹200

Step 3 — Supervision ₹1,200 on number of workers (30 : 20 : 10 = 3 : 2 : 1, total 6 parts).

• A = 1,200 × 3/6 = ₹600
• B = 1,200 × 2/6 = ₹400
• S = 1,200 × 1/6 = ₹200

Primary distribution summary:

Wait — re-add each department column carefully: A = 1,500 + 1,000 + 600 = ₹3,100; B = 1,000 + 800 + 400 = ₹2,200; S = 500 + 200 + 200 = ₹900. Cross-check: 3,100 + 2,200 + 900 = ₹6,200, which equals the total of all items (3,000 + 2,000 + 1,200 = 6,200). The distribution therefore balances.

Dual-solve check by columns rather than by items: A gets 3/6, 5/10 and 3/6 of the three items → 1,500 + 1,000 + 600 = ₹3,100; B gets 2/6, 4/10 and 2/6 → 1,000 + 800 + 400 = ₹2,200; S gets 1/6, 1/10 and 1/6 → 500 + 200 + 200 = ₹900. The three column totals sum to ₹6,200, matching the total of the three items (₹6,200), confirming the answer independently of the row working.

Students sometimes apportion every item on the same basis (e.g. number of workers throughout) instead of matching each item to its correct basis. Another slip is forgetting to include the service department S in the primary distribution — all departments, service included, receive a share at this stage.