# Approach

Making a working table would form the first step in our problem solving effort. Once the working table is built, the rest of the approach is stereotypical.

Factually, our problem solving capability is limited by our ability to interpret the problem. Whatever may be the way the problem is presented (what we call problem models), if we can arrange the information into the working table, the rest of the task becomes easy.

Understanding the meaning of the variance helps derive the formula for calculating the variance even if we fail recollecting.

## Recalculating Standards

Building the following working table amounts to recalculating standards for both actual inputs and actual outputs. It enables us to use the simplest formulae involving costs for deriving the variances. It helps us solve almost all problems in a similar manner.
Working Table
Standard Actual
for SO for AO for AI Total Idle
(Abnormal)
Productive
ST SR ST(AO) SC(AO) ST(AI) SC(AI) AT AR AC SC(AT) IT SC(IT) PT SC(PT)
Factor (AO) (AI)
Skilled
Semi-Skilled
Unskilled
STsk
STss
STus
SRsk
SRus
ST(AO)sk
ST(AO)ss
ST(AO)us
SC(AO)sk
SC(AO)ss
SC(AO)us
ST(AI)sk
ST(AI)ss
ST(AI)us
SC(AI)sk
SC(AI)ss
SC(AI)us
ATsk
ATss
ATus
ARsk
ARus
ACsk
ACss
ACus
SC(AT)sk
SC(AT)ss
SC(AT)us
ITsk
ITss
ITus
SC(IT)sk
SC(IT)ss
SC(IT)us
PTsk
PTss
PTus
SC(PT)sk
SC(PT)ss
SC(PT)us
Total STMix SPMix ST(AO)Mix SC(AO)Mix ST(AI)Mix SC(AI)Mix ATMix ARMix ACMix SC(AT)Mix ITMix SC(IT)Mix PTMix SC(PT)Mix
Output SO SO(AO) SO(AI) AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

1. (AO) =
 AO SO
2. ST(AO) = ST ×
 AO SO

3. SC(AO) = ST(AO) × SR

4. SO(AO) = AO

5. (AI) =
 AI SI
=
 PTMix STMix
6. ST(AI) = ST ×
 AI SI

7. SC(AI) = ST(AI) × SR

8. SO(AI) = SO ×
 AI SI
= SO × 1.16

9. SC(AT) = AT × SR

10. SC(IT) = IT × SR

11. PT = AT − IT

12. SC(PT) = PT × SR

## Wish not to recalculate standards

In the formulae, use the adjustment factors
 AO SO
for (AO) and
 AI SI
for (AI).

Additionally using T × R for C in the formulae may eliminate the need to build the cost column in the working table.

# Formulae that can be used in all cases

 Labor/Labour LCV LRPV LUV/LGEV LEV LITV LMV/GCV LYV/LSEV = = = = = = = SC(AO) SC(AT) SC(AO) SC(AO) SC(AI) SC(AO) − − − − − − AC AC SC(AT) SC(PT) SC(IT) SC(PT) SC(AI) Cost Variance Rate of Pay Variance Usage/Gross-Efficiency Variance Efficiency Variance Idle Time Variance Mix/Gang-Composition Variance Yield/Sub-Efficiency Variance

We can derive all other forms of the formulae from these.

• Keeping the suffix attached to quantity, replace
• SC with ST × SR
• AC with AT × AR

Eg : SC(AO) − AC, gives ST(AO) × SR − AT × AR

• To use formulae without having to recalculate standards, additionally replace
• (AO) with ×  AO SO
• (AI) with ×  AI SI
• (AT) with ×  AT ST
(whereby SC(AT) gives AT × SR)
• (PT) with ×  PT ST
(whereby SC(PT) gives PT × SR)
• (IT) with ×  IT ST
(whereby SC(IT) gives IT × SR)
ST(AO) × SR, gives ST ×  AO SO
× SR

Formulae containing the expression AT × SR or PT × SR or IT × SR should not be used for calculating the variance for the mix (total) in case where there are two or more labour/labor types being used.

# Problem

Three kinds of labourers/laborers Men, Women and Boys are required for the manufacture of a product. They are paid at the rate of 5 per hour, 4 per hour and 3 per hour respectively. The standards reveal that a gang of 25 men, 20 women and 40 boys are required to work for a time of 40 hrs over a week to bring out an output of 5,000 units.

During a 2 week period the actual production data revealed that there were 28 men, 20 women and 35 boys working in the gang and were paid @ 6, 3 and 3 per hour respectively. In achieving an output of 10,200 units, the average weekly work hours were 42.

There was a breakdown of power and no work was possible for 5 hours on a day. However, during this time the boys had been working as their work does not need power.

Calculate all possible variances relating to labour/labor.

# Working Notes - Working Table

## Calculation of work times

Particulars Men Women Boys Total
Standard/Budgeted
(a) Number Working
(b) Weekly Work Time (in hrs)
Total Weekly
Work Time (in hrs) (a) × (b)
Output

25
40

1,000

20
40

800

40
40

1,600

3,400
5,000
Actual
(c) Number Working
(d) Weekly Work Time (in hrs)
(e) Number of Weeks Working
(f) Time Lost (on a day) (in hrs)
Total
(g) Work Time (in hrs) (c) × (d) × (e)
(h) Idle Time (c) × (f)
(i) Productive Time (g) − (h)
Output

28
42
2
5

2,352
140
2,212

20
42
2
5

1,680
100
1,580

35
42
2
0

2,940
0
2,940

6,972
240
6,732
10,200

## Working Table

Working table incorporating the data in the problem and the calculated values including recalculated standards
Working Table with recalculated standards
Standard Actual
for SO for AO for AI Total Idle
(Abnormal)
Productive
ST SR ST(AO) SC(AO) ST(AI) SC(AI) AT AR AC SC(AT) IT SC(IT) PT SC(PT)
Factor 2.04 1.98
Men
Women
Boys
1,000
800
1,600
5
4
3
2,040
1,632
3,264
10,200
6,528
9,792
1,980
1,584
3,168
9,900
6,336
9,504
2,352
1,680
2,940
6
3
3
14,112
5,040
8,820
11,760
6,720
8,820
140
100
0
700
400
0
2,212
1,580
2,940
11,060
6,320
8,820
Total 3,400 6,936 26,520 6,732 25,740 6,972 27,972 27,300 240 1,100 6,732 26,200
Output 5,000
SO
10,200
SO(AO)
9,900
SO(AI)
10,200
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

1. (AO) =
 AO SO
=
 10,200 5,000
= 2.04
2. ST(AO) = ST ×
 AO SO
= ST × 2.04

3. SC(AO) = ST(AO) × SR

4. SO(AO) = AO

5. (AI) =
 AI SI
=
 PTMix STMix
=
 6,732 3,400
= 1.98
6. ST(AI) = ST ×
 AI SI
= ST × 1.98

7. SC(AI) = ST(AI) × SR

8. SO(AI) = SO ×
 AI SI
= SO × 1.98

9. SC(AT) = AT × SR

10. SC(IT) = IT × SR

11. PT = PT − IT

12. SC(PT) = PT × SR

13. SC/UO =
 SC(AO) AO
=
 26,520 10,200
= 2.6/unit

# Illustration - Solution

## Labor/Labour Cost Variance ~ LCV

LCV = SC(AO) − AC

Labor/Labour Cost Variance due to

 Men, LCVm = SC(AO)m − ACm = 10,200 − 14,112 = − 3,912 [Adv] Women, LCVw = SC(AO)w − ACw = 6,528 − 5,040 = + 1,488 [Fav] Boys, LCVb = SC(AO)b − ACb = 9,792 − 8,820 = + 972 [Fav] TLCV or LCVMix = − 1,452 [Adv] Labor/Labour Mix, LCVMix = SC(AO)Mix − ACMix = 26,520 − 27,972 = − 1,452 [Adv]

## Labor/Labour Rate of Pay Variance ~ LRPV

LRPV = SC(AT) − AC

Labor/Labour Rate of Pay Variance due to

 Men, LRPVm = SC(AT)m − ACm = 11,760 − 14,112 = − 2,352 [Adv] Women, LRPVw = SC(AT)w − ACw = 6,720 − 5,040 = + 1,680 [Fav] Boys, LRPVb = SC(AT)b − ACb = 8,820 − 8,820 = 0 TLRPV = − 672 [Adv] Labor/Labour Mix, LRPVMix = SC(AT)Mix − ACMix = 27,300 − 27,972 = − 672 [Adv]

## Labor/Labour Usage/Gross-Efficiency Variance ~ LUV/LGEV

LUV/LGEV = SC(AO) − SC(AT)

Labor/Labour Efficiency Variance due to

 Men, LUV/LGEVm = SC(AO)m − SC(AT)m = 10,200 − 11,760 = − 1,560 [Adv] Women, LUV/LGEVw = SC(AO)w − SC(AT)w = 6,528 − 6,720 = − 192 [Adv] Boys, LUV/LGEVb = SC(AO)w − SC(AT)w = 9,792 − 8,820 = + 972 [Fav] TLGUV/TLGEV = − 780 [Adv] Labor/Labour Mix, LUV/LGEVMix = SC(AO)Mix − SC(AT)Mix = 26,520 − 27,300 = − 780 [Adv]

## Labor/Labour Efficiency Variance ~ LEV

LEV = SC(AO) − SC(PT)

Labor/Labour Efficiency Variance due to

 Men, LEVm = SC(AO)m − SC(PT)m = 10,200 − 11,060 = − 860 [Adv] Women, LEVw = SC(AO)w − SC(PT)w = 6,528 − 6,320 = + 208 [Fav] Boys, LEVb = SC(AO)w − SC(PT)w = 9,792 − 8,820 = + 972 [Fav] TLUV/TLEV = + 320 [Fav] Labor/Labour Mix, LEVMix = SC(AO)Mix − SC(PT)Mix = 26,520 − 26,200 = + 320 [Fav]

## Labor/Labour Idle Time Variance ~ LITV

LITV = − SC(IT)

Labor/Labour Idle Time Variance due to

 Men, LITVm = − SC(IT)m = − 700 [Adv] Women, LEVw = − SC(IT)w = − 400 [Adv] Boys, LITVb = − SC(IT)w = 0 TITV = − 1,100 [Adv] Labor/Labour Mix, LITVMix = − SC(IT)Mix = − 1,100 [Adv]

## Labor/Labour Mix/Gang-Composition Variance ~ LMV/GCV

LMV/GCV = SC(AI) − SC(PT)

Labor/Labour Mix/Gang-Composition Variance due to

 Men, LMV/GCVm = SC(AI)m − SC(PT)m = 9,900 − 11,060 = − 1,160 [Adv] Women, LMV/GCVw = SC(AI)w − SC(PT)w = 6,336 − 6,320 = + 16 [Fav] Boys, LMV/GCVb = SC(AI)b − SC(PT)b = 9,504 − 8,820 = + 684 [Fav] TLMV/TGCV = − 460 [Adv] LMV/GCVMix = SC(AI)Mix − SC(PT)Mix = 25,740 − 26,200 = − 460 [Adv]

## Labor/Labour Yield/Sub-Efficiency Variance ~ LYV/LSEV

LYV/LSEV = SC(AO) − SC(AI)

Labor/Labour Yield/Sub-Efficiency Variance due to

 Men, LYV/LSEVm = SC(AO)m − SC(AI)m = 10,200 − 9,900 = + 300 [Fav] Women, LYV/LSEVw = SC(AO)w − SC(AI)w = 6,528 − 6,336 = + 192 [Fav] Boys, LYV/LSEVb = SC(AO)b − SC(AI)b = 9,792 − 9,504 = + 288 [Fav] TLYV/TLSUV/TLSEV = + 780 [Fav] Labor/Labour Mix, LYV/LSEVMix = SC(AO)Mix − SC(AI)Mix = 26,500 − 25,740 = + 780 [Fav]

# Solution (minimal detail)

## Labor/Labour Cost Variance

LCV = SC(AO) − AC

 Men, Women, Boys, 10,200 − 14,112 6,528 − 5,040 9,792 − 8,820 = = = − 3,912 [Adv] + 1,488 [Fav] + 972 [Fav] Mix/Total, 26,520 − 27,972 = − 1,452 [Adv]

## Labor/Labour Rate of Pay Variance

LRPV = SC(AT) − AC

 Men, Women, Boys, 11,760 − 14,112 6,720 − 5,040 8,820 − 8,820 = = = − 2,352 [Adv] + 1,680 [Fav] 0 Mix/Total, 27,300 − 27,972 = − 672 [Adv]

## Labor/Labour Usage/Gross-Efficiency Variance

LUV/LGEV = SC(AO) − SC(AT)

 Men, Women, Boys, 10,200 − 11,760 6,528 − 6,720 9,792 − 8,820 = = = − 1,560 [Adv] − 192 [Adv] + 972 [Fav] Mix/Total, 26,520 − 27,300 = − 780 [Adv]

## Labor/Labour Efficiency Variance

LEV = SC(AO) − SC(PT)

 Men, Women, Boys, 10,200 − 11,060 6,528 − 6,320 9,792 − 8,820 = = = − 860 [Adv] + 208 [Fav] + 972 [Fav] Mix/Total, 26,520 − 26,200 = + 320 [Fav]

## Labor/Labour Idle Time Variance

LITV = − SC(IT)

 Men, Women, Boys, = = = − 700 [Adv] − 400 [Adv] 0 Mix/Total, = − 1,100 [Adv]

## Labor/Labour Mix/Gang-Composition Variance

LMV/GCV = SC(AI) − SC(PT)

 Men, Women, Boys, 9,900 − 11,060 6,336 − 6,320 9,504 − 8,820 = = = − 1,160 [Adv] + 16 [Fav] + 684 [Fav] Mix/Total, 25,740 − 26,200 = − 460 [Adv]

## Labor/Labour Yield/Sub-Efficiency Variance

LYV/LSEV = SC(AO) − SC(AI)

 Men, Women, Boys, 10,200 − 9,900 6,528 − 6,336 9,504 − 8,820 = = = + 300 [Fav] + 192 [Fav] + 288 [Fav] Mix/Total, 26,500 − 25,740 = + 780 [Fav]

# Solution (alternative presentation)

Men Women Boys Mix/Total
LYV/LSEV

Men
Women
Boys
Mix
SC(AO)
10,200
6,528
9,792
26,500

SC(AI)
9,900
6,336
9,504
25,740
+ LMV/GCV

Men
Women
Boys
Mix
SC(AI)
9,900
6,336
9,504
25,740

SC(PT)
11,060
6,320
8,820
26,200

+ 300

− 1,160

+ 192

+ 16

+ 288

+ 684

+ 780

− 460
LEV

Men
Women
Boys
Mix
SC(AO)
10,200
6,528
9,792
26,520

SC(PT)
11,060
6,320
8,820
26,200
+ LITV

Men
Women
Boys
Mix
− SC(IT)

− 860

− 700

+ 208

− 400

+ 972

0

+ 320

− 1,100
LUV/LGEV

Men
Women
Boys
Mix
SC(AO)
10,200
6,528
9,792
26,520

SC(AT)
11,760
6,720
8,820
27,300
+ LRPV

Men
Women
Boys
Mix
SC(AT)
11,760
6,720
8,820
27,300

AC
14,112
5,040
8,820
27,972

− 1,560

− 2,352

− 192

+ 1,680

+ 972

0

− 780

− 672
LCV

Men
Women
Boys
Mix
SC(AO)
10,200
6,528
9,792
26,520

AC
14,112
5,040
8,820
27,972

− 3,912

+ 1,488

+ 972

− 1,452

# Verification

If adopting the first and second presentation methods, it would help building the following table to enable us to verify whether our workings are correct or not.
Formula Men Women Boys Mix/Total
LYV/LSEV
+ LMV/GCV
SC(AO) − SC(AI)
SC(AI) − SC(PT)
+ 300
− 1,160
+ 192
+ 16
+ 288
+ 684
+ 780
− 460
LEV
+ LITV
SC(AO) − SC(PT)
− SC(IT)
− 860
− 700
+ 208
− 400
+ 972
0
+ 320
− 1,100
LUV/LGEV
+ LRPV
SC(AO) − SC(AT)
SC(AT) − AC
− 1,560
− 2,352
− 192
+ 1,680
+ 972
0
− 780
− 672
LCV SC(AO) − AC − 3,912 + 1,488 + 972 − 1,452

## Simplest

One may use this as the simplest presentation of calculations, since all the amounts used in the formula are present in the working table.

If it is for verification purposes, we may avoid the formula column.

Adopt a presentation based on the examination you are attending and the proportion of marks allotted and time available to/for the problem.