WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE
  
Kosprys, verkoopprys, wins, verlies. BTW : antwoorde
  
MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES
  
Cost price, selling price, profit, loss. VAT : answers
  

  
Antwoord / Answer   1.

        N.B.  Die volgende afkortings word in die antwoorde, waar nodig, gebruik :
        N.B.  The following abbreviations are used, where necessary, in the answers :
  
                 KP / CP : kosprys / cost price   
  
                 AD% : persentasie afslag / percentage discount  
  
                 JB/YP : jy betaal / you pay  
  
                 P(R) : wins Rand / profit Rand  
  
                 BTW / VAT  
  
  
  
                 VP / SP  : verkoopprys / selling price
  
                 AD(R) : afslag gegee / discount given  
  
                 %P  : persentasie wins / percentage profit  
  
                 FP(R) : finale prys / final price  
  
  
  
  
  
  
      1.1  Afslag / Discount = Afslag % / Discount % × 
  
                                                Verkoopprys / Selling price
  
  
                                     a = AD%  ×  VP / SP
  
                                                 10
                                     a = R ───  ×  115
                                               100
  
                                        = 11,50
  
  
              Jy betaal / You pay = Verkoopprys / Selling price − 
  
                                               Afslag gegee / Discount given
  
  
                                          b = VP/SP  −  ADR
  
                                             = R115  −  R11,50
  
                                             = R11,50                              [ 1.1 ]
  
  
  
      1.3  Persentasie Afslag / Percentage Discount 
  
                       Afslag gegee / Discount given       100
                 =  ───────────────────  ×  ───
                       Verkoopprys / Selling price              1
  
                          ADR          100
             e  =  ──────  ×  ───  %
                        VP/SP           1
  
                       4,10           100
                =  ─────  ×  ───  %
                        63               1
  
                =  6,51  %
  
  
              Jy betaal / You pay = Verkoopprys / Selling price − 
  
                                               Afslag gegee / Discount given
  
  
                                          f = VP/SP  −  ADR
  
                                             = R63  −  R4,10
  
                                             = R58,90                              [ 1.3 ]
  
  
  
      1.5  Afslag gegee / Discount given 
  
                  = Verkoopprys / Selling price −   Jy betaal / You pay
  
              k  =  VP/SP − JB/YP
  
                  =  R794,00 − R730,48
  
                  =  R63,52
  
  
              Persentasie Afslag / Percentage Discount 
  
                       Afslag gegee / Discount given       100
                 =  ───────────────────  ×  ───
                       Verkoopprys / Selling price              1
  
                          ADR          100
             j  =  ──────  ×  ───  %
                        VP/SP           1
  
                       63,52        100
                =  ─────  ×  ───  %
                        794            1
  
                =  8  %                                                         [ 1.5 ]
  
  
  
      1.2  Afslag / Discount = Afslag % / Discount % × 
  
                                                Verkoopprys / Selling price
  
  
                                     c = AD%  ×  VP / SP
  
                                                 5
                                     a = R ───  ×  218,15
                                               100
  
                                        = 10,91
  
  
              Jy betaal / You pay = Verkoopprys / Selling price − 
  
                                               Afslag gegee / Discount given
  
  
                                          b = VP/SP  −  ADR
  
                                             = R218,15  −  R10,91
  
                                             = R207,24                              [ 1.2 ]
  
  
  
      1.4  Persentasie Afslag / Percentage Discount 
  
                       Afslag gegee / Discount given       100
                 =  ───────────────────  ×  ───
                       Verkoopprys / Selling price              1
  
                          ADR          100
             g  =  ──────  ×  ───  %
                        VP/SP           1
  
                      61,20         100
                =  ─────  ×  ───  %
                        816            1
  
                =  7,5  %
  
  
              Jy betaal / You pay = Verkoopprys / Selling price − 
  
                                               Afslag gegee / Discount given
  
  
                                          h = VP/SP  −  ADR
  
                                             = R816  −  R61,20
  
                                             = R754,80                              [ 1.4 ]
  
  
  
      1.6  Verkoopprys / Selling price
  
                  = Jy betaal / You pay  +  Afslag gegee / Discount given
  
              m =  JB/YP + ADR
  
                  =  R353,17 + R62,33
  
                  =  R415,50
  
  
              Persentasie Afslag / Percentage Discount 
  
                       Afslag gegee / Discount given       100
                 =  ───────────────────  ×  ───
                       Verkoopprys / Selling price              1
  
                          ADR          100
             n  =  ──────  ×  ───  %
                        VP/SP           1
  
                      62,33         100
                =  ─────  ×  ───  %
                     415,50          1
  
                =  15,00  %                                                         [ 1.6 ]
  
  
  
Antwoord / Answer   2.

  
      2.1  Wins (R) / Profit (R)
  
              = Persentasie wins/Percentage profit × Kosprys/Cost price
  
               a =  P% × KP/CP
  
                             8
                  = R ────  ×  45,52
                          100
  
                  = R 3,64
  
  
              Verkoopprys / Selling price 
  
                =  Kosprys / Cost price  +  Wins / Profit 
  
             b  =  KP/CP  +  P(R)  
  
                 =  R45,52  +  R 3,64 
  
                 =  R49,16       %                                                         [ 2.1 ]
  
  
      2.3  Persentasie wins / Percentage profit 
  
                               Wins / Profit                 100
                 =  ───────────────  ×  ───  %
                       Koopprys / Cost price            1
  
                          P(R)         100
             e  =  ──────  ×  ───  %
                        KP/CP           1
  
                       16,25         100
                =  ─────  ×  ───  %
                         25              1
  
                =  65,00  %
  
  
              Verkoopprys / Selling price  
  
                      = Kosprys / Cost price  +  Wins / Profit
  
                   f =  KP/CP  +  P(R)
  
  
                     =  R 25  +  R 16,25
  
  
                     =  R 41,25                                                     [ 2.3 ]
  
  
  
      2.5  Kosprys / Cost price 
  
                     =  Verkoopprys / Selling price  −  Wins / Profit
  
  
                  k =  VP/SP  −  P(R)
  
                     =  R 742,03  −  R 96,79
  
                     =  R 645,24
  
  
              Persentasie wins / Percentage profit 
  
                               Wins / Profit                 100
                 =  ───────────────  ×  ───  %
                       Koopprys / Cost price            1
  
                          P(R)           100
             m  =  ──────  ×  ───  %
                        KP/CP            1
  
                       96,79      100
                =  ─────  ×  ───  %
                     645,24          1
  
                =  15,00  %                                                         [ 2.5 ]
  
  
  
      2.7   As die wins % = 10% en die KP = R100 is die wins
  
              R10 en die verkoopprys = R110
  
              As die PR% = 10% en die VP/SP = R110 is die
  
              P(R) = R10 en die KP/CP = R100
  
  
  
  
      2.2  Wins (R) / Profit (R)
  
              = Persentasie wins/Percentage profit × Kosprys/Cost price
  
               c =  P% × KP/CP
  
                             25
                  = R ────  ×  25,80
                          100
  
                  = R 6,45
  
  
              Verkoopprys / Selling price 
  
                =  Kosprys / Cost price  +  Wins / Profit 
  
             b  =  KP/CP  +  P(R)  
  
                 =  R25,80  +  R 6,45 
  
                 =  R32,25       %                                                         [ 2.2]
  
  
      2.4  Kosprys / Cost price 
  
                     =  Verkoopprys / Selling price  −  Wins / Profit
  
  
                  g =  VP/SP  −  P(R)
  
                     =  R 428,61  −  R 107,07
  
                     =  R 321,54
  
  
              Persentasie wins / Percentage profit 
  
                               Wins / Profit                 100
                 =  ───────────────  ×  ───  %
                       Koopprys / Cost price            1
  
                          P(R)           100
             h  =  ──────  ×  ───  %
                        KP/CP            1
  
                       107,07      100
                =  ─────  ×  ───  %
                     321,54          1
  
  
                =  33,299  %                                                         [ 2.4 ]
  
  
  
      2.6  Wins / Profit
  
                     =  Verkoopprys / Selling price  −  Koopprys / Cost price
  
  
                  p =  VP/SP  −  KP/CP
  
                     =  R 25,08  −  R 21,25
  
                     =  R 3,83
  
  
              Persentasie wins / Percentage profit 
  
                               Wins / Profit                 100
                 =  ───────────────  ×  ───  %
                       Koopprys / Cost price            1
  
                          P(R)           100
             h  =  ──────  ×  ───  %
                        KP/CP            1
  
                       107,07      100
                =  ─────  ×  ───  %
                     321,54          1
  
                =  33,299  %                                                         [ 2.6 ]
  
  
  
      2.7   If the profit % = 10% and the CP = R100, the profit is
  
              R10 and the selling price = R110
  
              If the PR% = 10% and the VP/SP = R110, the
  
              profit = R10 and the KP/CP = R100
  
  
  
           As die / If the  PR% = 10%  en die / and the VP/SP = R110  is die / the KP/CP = R100  en die / and the P(R) = R10
  
           As / If PR% = 8,5% en / and VP/SP = R108,50  is / KP/CP = R100  en / and P(R) = R8,50
  
  
                                                                                                               100                                              8,50
           As / If PR% = 8,5% en / and VP/SP = R 1  is / KP/CP = R ──────    en / and P(R) = R ──────
                                                                                                             108,50                                         108,50
  
  
                                                                                                                     100                                                       8,50
           As / If PR% = 8,5% en / and VP/SP = R 52,34  is /  KP/CP = R ─────  ×  52,34 en / and P(R) = R ─────  ×  52,34
                                                                                                                   108,50                                                  108,50
  
  
           As die / If the  PR% = 8,5% en die / and the VP/SP = R52,34  is die / the KP/CP = R48,24  en die / and the P(R) = R4,10
  
  
                    q = R48,24 ;  r = R4,10                                                                                                                                                                    [ 2.7 ]
  
    
  
      2.8   As die wins % = 12,5% en die KP = R100 is die wins
  
              R12,50 en die verkoopprys = R112,50
  
              As die PR% = 12,50% en die VP/SP = R112,50 is die
  
              P(R) = R12,50 en die KP/CP = R100
  
  
  
  
      2.8   If the profit % = 12,50% and the CP = R100, the profit
  
              is R12,50 and the selling price = R112,50
  
              If the PR% = 12,50% and the VP/SP = R112,50, the
  
              profit = R12,50 and the KP/CP = R100
  
  
  
           As die / If the  PR% = 10%  en die / and the VP/SP = R110  is die / the KP/CP = R100  en die / and the P(R) = R10
  
           As die / If the  PR% = 12,5%  en die / and the VP/SP = R112,50  is die / the KP/CP = R100  en die / and the P(R) = R12,50
  
  
                                                                                                                                                      100                                                        12,50
           As die / If the  PR% = 12,5%  en die / and the VP/SP = R 1  is die / the KP/CP = R ──────      en die / and the P(R) = R ──────
                                                                                                                                                    112,50                                                     112,50
  
  
                                                                                                                                   100                                                                 12,50
           As / If PR% = 12,5% en / and VP/SP = R 36,68  is die / the KP/CP = R ─────  ×  36,68  en die / and the P(R) = R ─────  ×  36,68
                                                                                                                                 112,50                                                             112,50
  
  
           As die / If the  PR% = 12,5%  en die / and the VP/SP = R36,68  is die / the KP/CP = R32,60  en die / and the P(R) = R4,08
  
  
              s = R32,60 ;  t = R4,08                                                                                                                                                                          [ 2.8 ]
  
    
  
Antwoord / Answer   3.

  
      3.1  BTW / VAT   =  15% van / of  verkoopprys / selling price 
  
             BTW / VAT   =  15%  ×  VP/SP
  
                              a  =  15%  ×  VP/SP
  
                                         15
                                  =  ────  ×  R 15
                                        100
  
  
                                  =  R 2,25
  
  
            Finale prys / Final price 
  
                        =  Verkoopprys / Selling price  +  BTW / VAT
  
                     b =  VP/SP  +  BTW / VAT
  
                        =  R15  +  R2,25
  
                        =  R17,25                                              [ 3.1 ]
  
  
  
      3.3   As die BTW = 15% en die VP = R100 is die
  
              BTW R15,00 en die finale prys = R115,00
  
              As die BTW% = 15% en die finale prys = R115,00
  
              is die VP = R100,00 en die BTW = R15
  
  
  
  
      3.2  BTW / VAT   =  15% van / of  verkoopprys / selling price 
  
             BTW / VAT   =  15%  ×  VP/SP
  
                              c  =  15%  ×  VP/SP
  
                                         15
                                  =  ────  ×  R 36,25
                                        100
  
  
                                  =  R 5,44
  
  
            Finale prys / Final price 
  
                        =  Verkoopprys / Selling price  +  BTW / VAT
  
                     b =  VP/SP  +  BTW / VAT
  
                        =  R36,25  +  R5,44
  
                        =  R41,69                                              [ 3.2 ]
  
  
  
      3.3   If the VAT % = 12,50% and the SP = R100, the
  
              VAT is R15,00 and the final price = R115,50
  
              If the PR% = 15% and the final price = R115,00
  
              the SP = R100,00 and the VAT = R15
  
  
  
           As / If BTW/VAT% = 15% en / and finale prys / final price = R115  is die / the VP/SP = R100  en die / and the BTW/VAT = R15
  
                                                                                                                                100                                                                   15,0
           As / If BTW/VAT% = 15% e / and FP(R) = R 1  is die / the VP/SP = R ──────      en die / and the BTW / VAT = R ──────
                                                                                                                                115                                                                   115
  
  
                                                                                                                                100                                                               15,00
          As / If BTW/VAT% = 15%  en / and FP(R) = R 135,48  is / KP/CP = R ─────  ×  135,48  en / and BTW/VAT = R ─────  ×  135,48
                                                                                                                             115,00                                                           115,00
  
  
           As die / If the  BTW/VAT% = 15%  en die / and the FP(R) = R135,48  is die / the VP/SP = R117,81  en die / and the BTW/VAT = R17,67
  
  
               OF / OR 
                                                                              100                                                                                  15
                       Verkoopprys / Selling price  =  R ─────  ×  135,48     en die / and the  BTW/VAT =  R ─────  ×  135,48
                                                                              115                                                                                 115
  
  
                    Verkoopprys / Selling price  =  R 117,81     en die / and the  BTW/VAT =  R 17,67
     
  
                      e = R117,81 ;  f = R17,67                                                                                                                                                                       [ 3.3 ]
  
  
  
    
  
  
      3.4   As die BTW = 15% en die VP = R100 is die
  
              BTW R15,00 en die finale prys = R115,00
  
              As die BTW% = 15% en die finale prys = R115,00
  
              is die VP = R100,00 en die BTW = R15
  
  
  
  
      3.4   If the VAT % = 12,50% and the SP = R100, the
  
              VAT is R15,00 and the finkosval price = R115,50
  
              If the PR% = 15% and the kosvfinal price = R115,00
  
              the SP = R100,00 and the VAT = R15
  
  
  
           As / If BTW/VAT% = 15% en / and finale prys / final price = R115  is die / the VP/SP = R100  en die / and the BTW/VAT = R15
  
                                                                                                                                   100                                                                   15,0
           As / If BTW/VAT% = 15% en / and FP(R) = R 1  is die / the VP/SP = R ──────      en die / and the BTW / VAT = R ──────
                                                                                                                                   115                                                                   115
  
  
                                                                                                                               100                                                               15,00
          As / If BTW/VAT% = 15% en / and FP(R) = R 572,28  is / KP/CP = R ─────  ×  572,28  en / and BTW/VAT = R ─────  ×  572,28
                                                                                                                             115,00                                                           115,00
  
  
           As die  / If the  BTW/VAT% = 15%  en die / and the FP(R) = R572,28  is die / the VP/SP = R117,81  en die / and the P = R17,67
  
  
                  g = R497,63 ;  h = R74,65                                                                                                                                                                    [ 3.4 ]
  
    
  
      3.5  BTW / VAT   =  15% van / of  verkoopprys / selling price 
  
             BTW / VAT   =  15%  ×  VP/SP
  
                              a  =  15%  ×  VP/SP
  
                                         15
                                  =  ────  ×  R 804,51
                                        100
  
  
                                  =  R 120,68
  
  
            Finale prys / Final price 
  
                        =  Verkoopprys / Selling price  +  BTW / VAT
  
                     b =  VP/SP  +  BTW / VAT
  
                        =  R804,51  +  R120,68
  
                        =  R925,19                                              [ 3.5 ]
  
  
  
      3.6  BTW / VAT   =  15% van / of  verkoopprys / selling price 
  
             BTW / VAT   =  15%  ×  VP/SP
  
                              c  =  15%  ×  VP/SP
  
                                         15
                                  =  ────  ×  R 55,64
                                        100
  
  
                                  =  R 8,35
  
  
            Finale prys / Final price 
  
                        =  Verkoopprys / Selling price  +  BTW / VAT
  
                     b =  VP/SP  +  BTW / VAT
  
                        =  R55,64  +  R8,35
  
                        =  R63,99                                              [ 3.6 ]
  
  
  
      3.7   As die BTW = 15% en die VP = R100 is die
  
              BTW R15,00 en die finale prys = R115,00
  
              As die BTW% = 15% en die finale prys = R115,00
  
              is die VP = R100,00 en die BTW = R15
  
  
  
  
      3.7   If the VAT % = 12,50% and the SP = R100, the
  
              VAT is R15,00 and the final price = R115,50
  
              If the PR% = 15% and the final price = R115,00
  
              the selling price = R100,00 and the VAT = R15
  
  
  
           As / If BTW/VAT% = 15%  en / and finale prys / final price = R115  is / VP/SP = R100  en die / and the BTW/VAT = R15
  
                                                                                                                      100                                                         15,0
           As / If BTW/VAT% = 15% en / and FP(R) = R 1  is / VP/SP = R ──────      en / and BTW / VAT = R ──────
                                                                                                                      115                                                          115
  
  
                                                                                                                             100                                                  15,00
           As / If BTW/VAT% = 15% en / and FP(R) = R 92,66  is / KP/CP = R ───── × 92,66  en / and P(R) = R ───── × 92,66
                                                                                                                            115,00                                              115,00
  
  
           As die  / If the  BTW/VAT% = 15%  en die / and the FP(R) = R92,66  is die / the VP/SP = R80,57  en die / and the P = R12,09
  
  
              p = R80,57 ;  q = R12,09                                                                                                                                                                       [ 3.7 ]
  
    

  
Antwoord / Answer   4.

  
      4.1   Die koste van enige aantal kaartjies is die produk van die
  
              aantal kaartjies en die koste van een kaartjie.
  
                c = 5n
                                                                                               [ 4.1 ]
  
  
      4.2   Die inkomste van enige aantal kaartjies is agt
  
              maal die aantal kaartjies verkoop.
  
                a = 8q
                                                                                               [ 4.2 ]
  
  
      4.3   Die wins is die inkomste van die aantal kaartjies
  
              verkoop minus die koste om enige aantal kaartjies te koop.
  
                P = a - c = 8q - 5n
                                                                                            [ 4.3 ]
  
  
      4.4.1   q kan nie groter wees as n nie, want jy kan nie
  
                 meer kaartjies verkoop as wat jy het nie.
  
                                                                                            [ 4.4.1 ]
  
  
      4.4.2   As q = n is 8q > 5n, die inkomste is groter as
  
                 die uitgawe en jy maak nog steeds 'n wins.
  
                                                                                            [ 4.4.2 ]
  
  
      4.4.3   As q < n en 8q > 5n, maak jy nog steeds 'n wins.
  
                 As q < n en 8q = 5n, breek jy gelyk,
  
                 die inkomste = die uitgawe en wins = 0.
  
                 As q < n en 8q < 5n, maak jy 'n verlies,
  
                 die inkomste < die uitgawe.
  
                                                                                                 [ 4.4.3 ]
  
  
  
      4.1   The cost of any number of picture cards is the product
  
              of the number of cards and the cost for one card.
  
                c = 5n
                                                                                                          [ 4.1 ]
  
  
      4.2   The income from any number of picture cards is eight
  
              eight times the number of cards sold.
  
                a = 8q
                                                                                                          [ 4.2 ]
  
  
      4.3   The profit is the income from the cards sold minus
  
              the cost of any number of picture cards bought.
  
                P = a - c = 8q - 5n
                                                                                                          [ 4.3 ]
  
  
      4.4.1   q can not be greater than n, because you cannot
  
                 sell more cards than you bought.
  
                                                                                                     [ 4.4.1 ]
  
  
      4.4.2   If q = n then 8q > 5n, the income is greater than
  
                 the expenses and you still make a profit.
  
                                                                                                     [ 4.4.2 ]
  
  
      4.4.3   If q < n and 8q > 5n, you still make a profit.
  
                 If q < n and 8q = 5n, you break even,
  
                 the income = the expenses and profit = 0.
  
                 If q < n and 8q < 5n, you make a loss,
  
                 the income < the expenses.
  
                                                                                                     [ 4.4.3 ]
  
  

  
Antwoord / Answer   5.

  
      5.1   Wins per kaartje = verkoopprys − aankoopprys
  
                                         = R5,00 − R2,50
  
                                         = R2,50                                   [ 5.1 ]
  
  
                                                wins            100
      5.2   Persentasie wins = ─────  ×  ────  %
                                                koste            1
  
                                                2,50            100
                                          = ─────  ×  ────  %
                                                2,50            1
  
                                          = 100 %                                [ 5.2 ]
  
  
      5.3   Inkomste >= R4 500  , wins per kaartjie = R2,50 
  
              en n kaartjies moet per maand verkoop word
  
              R2,50 × n  =  R4 500
  
                                      4 500
                             n =  ─────          
                                       2,50
  
                                = 1 800                                [ 5.3 ]
  
  
      5.4   Nuwe koste = ou koste + 18%  R2,50
  
                                                         18
                                   = R2,50  +  ────  ×  R2,50
                                                        100
  
                                   = R2,95
  
      OF   Nuwe koste = 118% van die ou koste
  
                                                         118
                                  = R2,50  ×  ────
                                                         100
  
                                  = R2,95
  
             Nuwe wins = R5,00 − R2,95  = R2,05
  
                                               wins            100
             Persentasie wins = ─────  ×  ────  %
                                               koste            1
  
                                                2,05            100
                                          = ─────  ×  ────  %
                                                2,95            1
  
                                          = 69,4 %                                [ 5.4 ]
  
  
      5.5   R2,05 × n  =  R4 500
  
                                      4 500
                             n =  ─────          
                                       2,05
  
                                = 2 196                                             [ 5.5 ]
  
  
  
      5.6   Jy wil weer 100& wins maak. Jy moet dus
  
              'n wins maak wat gelyk is aan die produksiekoste,
  
               wat nou R2,95 per kaartjie is.
  
               Verkoopprys = R2,95 + R2,95 = R5,90             [ 5.6 ]
  
  
      5.1   Profit per card = selling price − cost price
  
                                      = R5,00 − R2,50
  
                                      = R2,50                                             [ 5.1 ]
  
  
                                                profit           100
      5.2   Percentage profit = ─────  ×  ────  %
                                                cost               1
  
                                                2,50           100
                                          = ─────  ×  ────  %
                                                2,50             1
  
                                          = 100 %                                         [ 5.2 ]
  
  
      5.3   Income >= R4 500  , profit per card = R2,50 
  
              and n cards must be sold per month
  
              R2,50 × n  =  R4 500
  
                                      4 500
                             n =  ─────          
                                       2,50
  
                                = 1 800                                                    [ 5.3 ]
  
  
      5.4   New cost = old cost + 18% of R2,50
  
                                                    18
                              = R2,50  +  ────  ×  R2,50
                                                   100
  
                              = R2,95
  
      OR   New cost = 118% of the old cost
  
                                                   118
                               = R2,50  ×  ────
                                                    100
  
                               = R2,95
  
              New profit = R5,00 − R2,95  = R2,05
  
                                               profit            100
             Percentage profit = ─────  ×  ────  %
                                               cost            1
  
                                                2,05            100
                                          = ─────  ×  ────  %
                                                2,95            1
  
                                          = 69,4 %                                [ 5.4 ]
  
  
      5.5   R2,05 × n  =  R4 500
  
                                      4 500
                             n =  ─────          
                                       2,05
  
                                = 2 196                                             [ 5.5 ]
  
  
  
      5.6   You again want to make a profit of 100&. Therefore
  
               you have to make a profit which is eqal to the
  
               production cost, which is now R2,95 per card.
  
               Selling price = R2,95 + R2,95 = R5,90              [ 5.6 ]