How to approach it
- Build total machine hours per department: units × hours per unit for each product, then add.
- Allocate each overhead on its stated basis (machine hours, area, percentages).
- Set up the two simultaneous equations for the service departments and solve.
- Reapportion the solved totals to production departments using their percentages; check the grand total is unchanged.
Key rules to apply
- Simultaneous equations: S1 = own overhead + share of S2; S2 = own overhead + share of S1.
- Repeated distribution gives the same answer but only use it if allowed.
Common mistakes
Drawn from the examiners' comments for this sitting (summarised in our words) and from typical errors on this topic.
- Apportioning on hours per unit instead of total machine hours (examiners' point).
- Using repeated distribution when simultaneous equations were required.
- Not checking that total overhead after reapportionment equals total before.
Similar question with worked solution
Written by us with our own numbers; it tests the same skills as Q5 without copying it.
Original practice question
Reciprocal service departments
After allocation: production X Rs 50,000, production Y Rs 40,000, service S1 Rs 20,000, service S2 Rs 15,000. S1 serves X 50%, Y 30%, S2 20%. S2 serves X 40%, Y 40%, S1 20%.
Required: Reapportion service costs using simultaneous equations.
Worked solution
S1 = 20,000 + 0.2 S2; S2 = 15,000 + 0.2 S1. Substituting: S1 = 23,000 + 0.04 S1, so S1 = 23,958.33 and S2 = 19,791.67.
| Department | Rs |
|---|---|
| X: 50,000 + 0.5 × 23,958.33 + 0.4 × 19,791.67 | 69,895.83 |
| Y: 40,000 + 0.3 × 23,958.33 + 0.4 × 19,791.67 | 55,104.17 |
| Total (check) | 125,000.00 |
Answer: X Rs 69,896; Y Rs 55,104.