Antwoorde / Answers 1
1.1 VP/SP = KP/CP + W/P
= KP/CP + W/P% × KP/CP
45
= R 23,10
+ 23,10 X ────
100
= R 33,50
a = R 33,50
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 33,50 ─ R 23,10
= R 10,40
b = R 10,40
OF / OR
W/P = W/P% X KP/CP
45
= R 23,10 X ────
100
= R 10,40
b = R 10,40
[ 1. ]
1.3 VP/SP = KP/CP + W/P
= R 1 186,00 + R 395,29
= R 1 581,29
e = R 1 581,29
[ 1. ]
W/P X 100
W/P% = ──────────
KP/CP
395,29 X 100
= ──────────
1 186
= 33,33%
f = 33,33%
[ 1. ]
1.5 KP/CP = VP/SP ─ W/P
= R 63,18 ─ 34,46
= R 28,72
k = R 28,72
[ 1. ]
W/P X 100
W/P% = ──────────
VP/SP ─ W/P
34,46 X 100
= ──────────
63,18 ─ 34,46
= 119,99%
m = 120,00%
[ 1. ]
1.7 VP/SP = KP/CP + W/P
= KP/CP + KP/CP X WP%
= KP/CP(100 + WP%)
100 X VP/SP
KP/CP = ───────────
(100 + WP%)
100 X 171,82
= ───────────
(100 + 38,5)
= 124,06
q = R124,06
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 171,82 ─ 124,06
= R 47,76
r = R 47,76
[ 1. ]
1.9 VP/SP = KP/CP + W/P
= KP/CP + W/P% × KP/CP
33
= R 2,75
+ 2,75 X ────
100
= R 3,66
u = R 3,66
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 3,66 ─ R 2,75
= R 0,91
v = R 0,91
OF / OR
W/P = W/P% X KP/CP
33
= R 2,75 X ────
100
= R 0,91
v = R 0,91
[ 1. ]
1.11 KP/CP = VP/SP ─ W/P
= R 14 424,74 ─ R 1 881,49
= R 12 543,25
y = R 12 543,25
[ 1. ]
W/P X 100
W/P% = ─────────
KP/CP
1 881,49 X 100
= ────────────
12 543.25
= 15 %
z = 15 %
[ 1. ]
100 X VP/SP
1.13
KP/CP = ─────────── sien / see 1.7
(100 + WP%)
100 X 524,20
= ───────────
(100 + 320)
= 124,81
cc = R 124,81
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 524,20 ─ R 124,81
bb = R 399,39
[ 1. ]
1.15 KP/CP = VP/SP ─ W/P
= R 65,24 ─ R 21,16
= R 44,08
hh = R 44,08
[ 1. ]
W/P X 100
W/P% = ─────────
KP/CP
21,16 X 100
= ────────────
44,08
= 48 %
gg = 48 %
[ 1. ]
1.2 VP/SP = KP/CP + W/P
= KP/CP + W/P% × KP/CP
40
= R 871,20
+ 871,20 X ────
100
= R 1 219,68
c = R 1 219,68
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 1 219,68 ─ R 871,20
= R 348,48
d = R 348,48
OF / OR
W/P = W/P% X KP/CP
40
= R 871,10 X ────
100
= R 348,48
d = R 348,48
[ 1. ]
1.4 VP/SP = KP/CP + W/P
= R 43,60 + R 10,90
= R 54,50
g = R 54,50
[ 1. ]
W/P X 100
W/P% = ──────────
KP/CP
10,90 X 100
= ──────────
43,60
= 25%
h = 25%
[ 1. ]
1.6 KP/CP = VP/SP ─ W/P
= R 515,21 ─ 202,96
= R 312,25
n = R 312,25
[ 1. ]
W/P X 100
W/P% = ──────────
KP/CP
202,96 X 100
= ──────────
312,25
= 65,00%
p = 65,00%
[ 1. ]
1.8 VP/SP = KP/CP + W/P
= KP/CP + KP/CP X WP%
= KP/CP(100 + WP%)
100 X VP/SP
KP/CP = ───────────
(100 + WP%)
100 X 61,07
= ───────────
(100 + 14,2)
= 53,48
s = R53,48
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 61,07 ─ 53,48
= R 7,59
t = R 7,59
[ 1. ]
1.10 VP/SP = KP/CP + W/P
= R 8,36 + R 2,76
= R 11, 12
w = R 11, 12
[ 1. ]
W/P X 100
W/P% = ─────────
KP/CP
2,76 X 100
= ─────────
8,36
= 33,01 %
x = R 11, 12
[ 1. ]
100 X VP/SP
1.12
KP/CP = ─────────── sien / see 1.7
(100 + WP%)
100 X 39,89
= ───────────
(100 + 40)
= 28,47
aa = R 28,47
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 39,89 ─ R 28,47
bb = R 11,40
[ 1. ]
1.14 VP/SP = KP/CP + W/P
= KP/CP + W/P% × KP/CP
65
= R 22,39
+ 22,39 X ────
100
= R 36,94
ee = R 36,94
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 36,94 ─ R 22,39
= R 14,55
ff = R 14,55
OF / OR
W/P = W/P% X KP/CP
65
= R 22,39 X ────
100
= R 14,55
ff = R 14,55
[ 1. ]
1.16 VP/SP = KP/CP + W/P
= KP/CP + W/P% × KP/CP
250
= R 27,08
+ 27,08 X ────
100
= R 94,78
kk = R 94,78
[ 1. ]
W/P = VP/SP ─ KP/CP
= R 94,78 ─ R 27,08
= R 67,70
ff = R 67,70
OF / OR
W/P = W/P% X KP/CP
250
= R 27,08 X ────
100
= R 67,70
ff = R 67,70
[ 1. ]
Antwoorde / Answers 2
2.1 W/P = VP/SP ─ KP/CP
= R 78,61 ─ R58,23
= R 20,38
OF / OR
W/P = KP/CP X W/P%
35
= R 58,23 X ────
100
= R 20,38
a = R 20,38
[ 2 ]
A/D = A/D% X VP/SP
10
= ──── X R 78,61
100
= R 7,86
b = R 7,86
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 78,61 ─ R 7,86
= R 70,75
c = R 70,75
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 70,75 ─ R 58,23
= R 12,52
d = R 12,52
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
12,52 100
= ───── X ────
58,25 1
= 22,5%
e = 22,5%
[ 2 ]
2.3 W/P = VP/SP ─ KP/CP
= R 2,77 ─ R2,08
= R 0,69
OF / OR
W/P = KP/CP X W/P%
33,33
= R 2,77 X ─────
100
= R 0,69
n = R 0,69
[ 2 ]
A/D = VP/SP X A/D%
15
= R 2,77 X ────
100
= R 0,42
p = R 0,42
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 2,77 ─ R 0,42
= R 2,35
q = R 2,35
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 2,35 ─ R 2,08
= R 0,27
r = R 0,27
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
0,27 100
= ───── X ────
2,08 1
= 12,98%
s = 12,98%
[ 2 ]
W/P 100
2.5
W/P% = ───── X ────
KP/CP 1
53,32 100
= ───── X ────
86 1
= 62,00%
y = 62,00%
[ 2 ]
A/D 100
A/D% = ───── X ────
VP/SP 1
16,72 100
= ────── X ────
139,32 1
= 12,00%
z = 12,00%
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 139,32 ─ R 16,72
= R 123,00
aa = R 123,00
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 123,00 ─ R 86,00
= R 37,00
bb = R 37,00
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
37,00 100
= ───── X ────
86,00 1
= 43,02%
cc = 43,02%
[ 2 ]
2.7 VP/SP = KP/CP + W/P
= R 832,42 ─ R1 248,63
= R 2 081,05
OF / OR
VP/SP = KP/CP + KP/CP X W/P%
= KP/CP(1 + W/P%)
150
= R 832,42(1 + ──── )
100
= R 2 081,05
kk = R 2 081,05
[ 2 ]
A/D = VP/SP X A/D%
25
= R 2 081,05 X ────
100
= R 520,26
mm = R 520,26
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 2 081,05 ─ R 520,26
= R 1 560,79
nn = R 1 560,79
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 1 560,79 ─ R 832,00
= R 728,79
pp = R 728,79
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
728,79 100
= ───── X ────
832,00 1
= 87,59%
qq = 87,59%
[ 2 ]
2.9 VP/SP = KP/CP + W/P
= R 8,64 ─ R4,75
= R 13,39
OF / OR
VP/SP = KP/CP + KP/CP X W/P%
= KP/CP(1 + W/P%)
55
= R 8,64(1 + ──── )
100
= R 13,39
kk = R 13,39
[ 2 ]
A/D = VP/SP X A/D%
5
= R 13,39 X ────
100
= R 0,67
xx = R 0,67
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 13,39 ─ R 0,67
= R 12,72
yy = R 12,72
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 12,72 ─ R 8,64
= R 4,08
zz = R 4,08
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
4,08 100
= ───── X ────
8,64 1
= 47,22%
ab = 47,22%
[ 2 ]
2.2 W/P = VP/SP ─ KP/CP
= R 173,11 ─ R123,65
= R 49,46
OF / OR
W/P = KP/CP X W/P%
40
= R 123,65 X ────
100
= R 49,46
f = R 49,46
[ 2 ]
A/D = VP/SP X A/D%
12
= R 173,11 X ────
100
= R 20,77
g = R 20,77
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 173,11 ─ R 20,77
= R 152,34
h = R 152,34
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 152,34 ─ R 123,65
= R 28,69
k = R 28,69
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
28,69 100
= ───── X ────
123,65 1
= 23,20%
e = 22,5%
[ 2 ]
W/P 100
2.4
W/P% = ───── X ────
KP/CP 1
11,43 100
= ───── X ────
13,45 1
= 84,98%
t = 12,98%
[ 2 ]
A/D 100
A/D% = ───── X ────
VP/SP 1
2,49 100
= ───── X ────
24,88 1
= 10,01%
u = 10,01%
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 24,88 ─ R 2,49
= R 22,39
v = R 22,39
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 22,39 ─ R 13,45
= R 8,94
w = R 8,94
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
8,94 100
= ───── X ────
13,45 1
= 66,47%
x = 66,47%
[ 2 ]
W/P 100
2.6
W/P% = ───── X ────
KP/CP 1
662,40 100
= ────── X ────
207,00 1
= 320%
dd = 320%
[ 2 ]
A/D 100
A/D% = ───── X ────
VP/SP 1
130,41 100
= ────── X ────
869,40 1
= 15%
ee = 15%
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 869,40 ─ R 130,41
= R 738,99
ff = R 738,99
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 738,99 ─ R 207,00
= R 531,99
gg = R 531,99
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
531,99 100
= ────── X ────
207,00 1
= 257%
hh = 257%
[ 2 ]
2.8 VP/SP = KP/CP + W/P
= R 906,88 + R2 539,26
= R 3 446,14
OF / OR
VP/SP = KP/CP + KP/CP X W/P%
= KP/CP(1 + W/P%)
280
= R 906,88(1 + ──── )
100
= R 3 446,14
rr = R 3 446,14
[ 2 ]
A/D = VP/SP X A/D%
32
= R 3 446,14 X ────
100
= R 1 102,76
ss = R 1 102,76
[ 2 ]
NVP/SP = VP/SP ─ A/D
= R 3 446,14 ─ R 1 102,76
= R 2 343,38
tt = R 2 343,38
[ 2 ]
NW/P = NVP/SP ─ KP/CP
= R 2 343,38 ─ R 906,88
= R 1 436,50
uu = R 1 436,50
[ 2 ]
NW/P 100
NW/P% = ───── X ────
KP/CP 1
1 436,50 100
= ─────── X ────
906.88 1
= 158,40%
vv = 158,40%
[ 2 ]
Antwoorde / Answers 3
3.1.1
VP/SP = KP/CP + KP/CP X W/P%
= KP/CP(1 + W/P%)
10
= R 18,52(1 + ──── )
100
= R 20,37
[ 3 ]
3.2.1
NKP/CP = KP/CP + verhoging / increase
= KP/CP(1 + 70% van / of KP/CP)
70
= R 18,52(1 + ──── )
100
= R 31,48
[ 3 ]
3.2.3
W/P = VP/SP ─ KP/CP
= R 34,63 ─ R 31,48
= R 3,15
OF / OR
W/P = KP/CP X W/P%
10
= R 31,48 X ────
100
= R 3,15
[ 3 ]
3.1.2
W/P = VP/SP ─ KP/CP
= R 20,37 ─ R 18,52
= R 1,85
OF / OR
W/P = KP/CP X W/P%
10
= R 18,52 X ────
100
= R 1,85
[ 3 ]
3.2.2
VP/SP = KP/CP + KP/CP X W/P%
= KP/CP(1 + W/P%)
10
= R 31,48(1 + ──── )
100
Antwoorde / Answers 4
4.1 Verhoging / Increase = nuwe prys / new price ─ ou prys / old price
= R5,75 ─ R5,40
= R0,35
[ 4 ]
prysverhoging / increase in price 100
4.2 Persentasie verhoging / Percentage increase = ────────────────────── X ──── %
ou prys / old price 1
0,35 100
= ───── X ──── %
5,40 1
= 6,45 %
[ 4 ]
4.3 Nuwe prys / New price = ou prys / old price + 12% van ou prys / 12% of old price
12
= R 5,40 + ──── X 5,40
100
= R 5,40 + R 0,65
= R 6,05
[ 4 ]
Antwoorde / Answers 5
5.1 Nuwe eenheidsprys / New price per unit = ou prys / old price + 12% van ou prys / 12% of old price
8,75
= R 0,28 + ──── X 5,40
100
= R 0,28 + R 0,0245
= R 0,30
[ 5 ]
5.2 Nuwe koste / New cost = koste per eenheid / cost per unit X aantal eenhede / number of units
= R 0,30 X 850
= R 255,00
[ 5 ]
Antwoorde / Answers 6
6.1 Nuwe eenheidsprys / New price per unit = ou prys / old price + 13,5% van ou prys / 13,5% of old price
13,5
= R 0,66 + ──── X 5,40
100
= R 0,66 + R 0,0891
= R 0,75
[ 6 ]
6.2 Opsie 1 / Option 1 :
Nuwe eenheidsprys eerste jaar / New price per unit first year = ou prys / old price + 30% van ou prys / 30% of old price
30
= R 0,75 + ──── X 0,75
100
= R 0,75 + R 0,225
= R 0,975
Nuwe eenheidsprys tweede jaar / New price per unit second year = ou prys / old price + 30% van ou prys / 30% of old price
20
= R 0,98 + ──── X 0,98
100
= R 0,98 + R 0,196
= R 1,18
Opsie 2 / Option 2 :
Nuwe eenheidsprys / New price per unit = ou prys / old price + 13,5% van ou prys / 13,5% of old price
50
= R 0,75 + ──── X 0,75
100
= R 0,75 + R 0,375
= R 1,13
Die eerste jaar kos opsie 1
R1,13 - R0,98 = R0,15 minder per eenheid.
Die tweede jaar kos opsie 1
R1,18 - R1,13 = R0,05 meer per eenheid.
Oor die twee jaar periode is Opsie 1 dus
10 sent per eenheid goedkoper as opsie 2.
Opsie 1 is dus die beste opsie.
[ 6 ]
During the first year option 1 costs
R1,13 - R0,98 = R0,15 less per unit.
During the second year option 1 costs
R1,18 - R1,13 = R0,05 more per unit.
Over the two year period Opsie 1 is thus
10 cent per unit cheaper than Option 2.
Option 1 is thus the better option.
[ 6 ]
Antwoorde / Answers 7
7.1 Maandelikse koste vir diesel / Monthly cost for diesel = 8 000 ℓ X R14,94 per ℓ
= R 119 520
[ 7 ]
7.2 Nuwe prys / New price = ou prys / old price + verhoging / increase
= R 14,94 + R 0,45
= R 15,39
[ 7 ]
7.3 Nuwe maandelikse koste vir diesel / New monthly cost for diesel = 8 000 ℓ X R15,39 per ℓ
= R 123 120
[ 7 ]
7.4 Persentasie verhoging - diesel / Percentage increase - diesel
verhoging / increase 100
Persentasie verhoging / Percentage increase = ─────────────── X ──── %
ou prys / old price 1
0,45 100
= ───── X ──── %
14,94 1
= 3,01 %
Verhoging in maandelikse koste / Increase in monthly cost = R 123 120 ─ R 119 520
= R 3 600
Persentasie verhoging - maandelikse koste / Percentage increase - monthly cost
verhoging / increase 100
Persentasie verhoging / Percentage increase = ─────────────── X ──── %
ou koste / old cost 1
3 600 100
= ─────── X ──── %
119 520 1
= 3,01 %
[ 7 ]