Question

The following are the details for a job which is expected to be completed within 50 weeks.

Grade of Workers	Standard		Actual
	No. of Workers	Wage Rate Per Worker (Weekly) (Rs.)	No. of Workers	Wage Rate Per Worker (Weekly) (Rs.)
Skilled	80	75	70	80
Semi-skilled	40	50	40	60
Unskilled	50	35	50	20

55 weeks were taken to complete the job.
Calculate the various Labour Variances.

Answer 1

Grade of Workers	Standard			Actual			Standard Proportion of Actual Weeks
	Weeks	Rate (Rs.)	Total (Rs.)	Weeks	Rate (Rs.)	Total (Rs.)
Skilled	80 x 50 = 4,000	75	3,00,000	70 x 55 = 3,850	80	3,08,000	4,141
Semi-skilled	40 x 50 = 2,000	50	1,00,000	40 x 55 = 2,200	60	1,32,000	2,071
Unskilled	50 x 50 = 2,500	35	87,500	50 x 55 = 2,750	20	55,000	2,588
	8,500		4,87,500	8,800		4,95,000	8,800

(a) Labour Rate Variance = (SR - AR) x Actual Time
Skilled : (75 - 80) x 3,850 weeks = Rs. 19,250 (A)
Semi-skilled : (50- 60) x 2,200 weeks = Rs. 22,000 (A)
Unskilled : (35 - 20) x 2,750 weeks · = Rs. 41,250 (F)
NIL

(b) Labour Efficiency Variance = (Std. Time - Actual Time) x SR
Skilled : (4,000 weeks - 3,850 weeks) x 75 = Rs. 11.250 (F)
Semi-skilled : (2,000 weeks - 2,200 weeks) x 50 = Rs. 10,000 (A)
Unskilled : (2,500 weeks - 2,750 weeks) x 35 = Rs. 8,750 (A)
Rs. 7,500 (A)

(c) Labour Cost Variance= SC - AC
Skilled : Rs. 3,00,000 - Rs. 3,08,000 = Rs. 8,000 (A)
Semi-skilled : Rs. 1,00,000 - Rs. 1,32,000 = Rs. 32,000 (A)
Unskilled : Rs. 87,500 - Rs. 55,000 = Rs. 32,500 (F)
Rs. 7,500 (A)

(d) Labour Mix Variance = SR x Difference in Mix
Skilled : 75 x (4,141 - 3,850) = Rs. 21,825 (F)
Semi-skilled : 50 x (2,071 - 2,200) = Rs. 6,450 (A)
Unskilled : 35 x (2,588 - 2, 750) = Rs. 5,670 (A)
Rs. 9,705 (F)

Answers:
(a) Labour Rate Variance = Rs. NIL.
(b) Labour Efficiency Variance = Rs. 7,500 (A).
(c) Labour Cost Variance = Rs. 7,500 (A).
(d) Labour Mix Variance = Rs. 9,705 (F).

Verification :
LRV + LEV - LCV
∴ Rs. (NIL) + Rs. 7,500 (A) = LCV
Rs. 7,500 (A)  = Rs. 7,500 (A)

Working Notes :
(1) Standard Proportion of Actual Weeks (8,800 weeks) are distributed among the three grades of workers in the ratio of 4,000 : 2,0QO : 2,500 i.e. (8 : 4 : 5) in the following way.

Skilled `=8,800xx8/17=4,141. `

Senii-skilled `=8,800xx4/17=2,071. `

Unskilled `=8,800xx5/17=2,588. `