Question 3 (c)
Labour cost, rate, efficiency and mix variances for a gang
12 marks
- Time to write
- About 24 minutes
Question
Question 3 (c) · 12 marks100 skilled, 40 semi-skilled and 60 unskilled workmen were to work so that a contract job could be completed within 30 weeks. The standard weekly wages Rs. 60, Rs. 35 and Rs. 25 respectively. The job was actually finished in 32 weeks by 80 skilled workmen, 50 semi-skilled and 70 unskilled workmen were paid weekly wages of Rs. 66, Rs. 40 and Rs. 22 respectively.
Calculate these Variances:
Cost Variance of Labour
Rate Variance of Labour
Efficiency Variance of Labour
Mix Variance of Labour
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
Two sentences are printed incomplete and are kept so. The second ("The standard weekly wages Rs....") has no verb; it is read as the standard weekly wage rates of the three grades. The third has no "who" before "were paid"; it is read as: the job was completed in 32 weeks by the stated workmen, who were paid the stated weekly wages.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Working: standard and actual cost 2 marks 3 min
- 2 Labour cost variance 2 marks 3 min
- 3 Labour rate variance 2½ marks 4 min
- 4 Labour efficiency variance 2½ marks 4 min
- 5 Labour mix variance with RSH 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 3 min
Try it first. About 24 minutes for 12 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Time is measured in worker-weeks. The standard is for the whole job, and the job was completed, so the standard cost of the actual output is the standard for the job. F = favourable, A = adverse.
| Category | Standard worker-weeks (SH) | Standard rate (₹) | Standard cost (₹) | Actual worker-weeks (AH) | Actual rate (₹) | Actual cost (₹) |
|---|---|---|---|---|---|---|
| Skilled | 100 × 30 = 3,000 | 60 | 1,80,000 | 80 × 32 = 2,560 | 66 | 1,68,960 |
| Semi-skilled | 40 × 30 = 1,200 | 35 | 42,000 | 50 × 32 = 1,600 | 40 | 64,000 |
| Unskilled | 60 × 30 = 1,800 | 25 | 45,000 | 70 × 32 = 2,240 | 22 | 49,280 |
| Total | 6,000 | 2,67,000 | 6,400 | 2,82,240 |
Revised standard worker-weeks (RSH): the actual 6,400 in the standard ratio 100: 40: 60 (50%: 20%: 30%) = skilled 3,200, semi-skilled 1,280, unskilled 1,920.
(i) Labour cost variance = Standard cost − Actual cost = ₹2,67,000 − ₹2,82,240 = ₹15,240 A
(ii) Labour rate variance = AH × (SR − AR)
| Category | Working | Variance (₹) |
|---|---|---|
| Skilled | 2,560 × (60 − 66) | 15,360 A |
| Semi-skilled | 1,600 × (35 − 40) | 8,000 A |
| Unskilled | 2,240 × (25 − 22) | 6,720 F |
| Total | 16,640 A |
(iii) Labour efficiency variance = SR × (SH − AH)
| Category | Working | Variance (₹) |
|---|---|---|
| Skilled | 60 × (3,000 − 2,560) | 26,400 F |
| Semi-skilled | 35 × (1,200 − 1,600) | 14,000 A |
| Unskilled | 25 × (1,800 − 2,240) | 11,000 A |
| Total | 1,400 F |
(iv) Labour mix variance = SR × (RSH − AH)
| Category | Working | Variance (₹) |
|---|---|---|
| Skilled | 60 × (3,200 − 2,560) | 38,400 F |
| Semi-skilled | 35 × (1,280 − 1,600) | 11,200 A |
| Unskilled | 25 × (1,920 − 2,240) | 8,000 A |
| Total | 19,200 F |
The rest of the efficiency variance is the labour yield (sub-efficiency) variance = SR × (SH − RSH) = 60 × (−200) + 35 × (−80) + 25 × (−120) = ₹17,800 A; mix ₹19,200 F + yield ₹17,800 A = efficiency ₹1,400 F.
| Variance | ₹ |
|---|---|
| Labour rate variance | 16,640 A |
| Labour efficiency variance | 1,400 F |
| Labour cost variance | 15,240 A |
Check: rate ₹16,640 A + efficiency ₹1,400 F = cost ₹15,240 A.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Working: standard and actual cost | 2 |
| 2 | Labour cost variance | 2 |
| 3 | Labour rate variance | 2.5 |
| 4 | Labour efficiency variance | 2.5 |
| 5 | Labour mix variance (with RSH) | 3 |
| Total | 12 |
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