Интерна Скрипта По Математика Во Угостителството

( )

, 2012

iii

............................................................................................... v

I ....................................................................... 7 1. ......................................................................................... 8 2. .......................................................................................... 8

2.1. ................................................................. 8 2.2. .................................................................. 8

3. ................................................................. 8 4. ................................................................................. 9 5. .......................................................... 9 6. ................................................................................. 11 . 1 .............................................................................................. 13 . 2 .............................................................................................. 15

II ..................................................... 17 1. ........................................................................ 18 2. .......................................................................... 18

2.1. ........................................................... 18 2.2. ........................................................ 18

3. ........................................................................ 21 4. ............................................ 21 . 3 .............................................................................................. 25 . 4 .............................................................................................. 27

III .......................................................................... 29 1. ........................... 30

1.1. ............................................................. 30 1.2. .............................................................. 31 1.3. .............................................................. 32 1.4. .................................................................................. 33 1.5. ....................................................................................... 34

. 5 .............................................................................................. 35 . 6 .............................................................................................. 37

iv

IV ............................................................................ 39 1. ........................................................................ 40 2. .......................................... 40 . 7 .............................................................................................. 43

V ........................................... 45 1. .................................................................... 46 2. ..................................................................... 46 3. ................................................................................... 46 4. / ................................................... 46

4.1. / / .......................... 47 4.2. / / ........................ 47 4.3. / / ........................ 48

. 8 .............................................................................................. 51

VI ................................ 53 1. ..................................................................................... 54 2. ........................................................................ 55 3. ......................................................................... 55

3.1. ............................................................ 56 3.2. .......................................................... 56 3.3. .......................................................... 57

. 9 .............................................................................................. 59

VII ........................................................................................ 61 1. .............................................................................. 62 2. ............................................... 62 3. .............................................................................. 62

3.1. ......................................... 62 3.2. ................................... 63 3.3. ....................... 63 3.3.1. () .......................... 63 3.3.2. ................................................ 65 3.3.3. .......................... 67 3.3.4. .... 67

. 10 ............................................................................................ 71 . 11 ............................................................................................ 73 . 12 ............................................................................................ 75

v

- - . . . , , . , . , .

. , , . . . , . , . , . , , .

vi

, , :

o ;

o , ;

o , , . , , , .

, 2012 .

7

I :

1. 2.

2.1. 2.2.

3. 4. 5. 6.

, :

o ; o ; o ; o ; o ; o ; o .

8

1.

. .

2.

2.1.

.

. , .

a b = d

2.2.

.

. .

a : b = q

=

3.

, .

: (1) .

a : b = q 8:4=2

. . = 8.2 : 4.2 = 2 :

9

a : b = q 8:4=2

:

=

8

2:

4

2= 2

(2) . a : b = q c : d = q 6:3=2 8:4=2 q, 2.

(3) , .

a : b 8:2=4 c : d 15:3=5

e : f 12:4=3

3:1=3

: ace : bde (8.15.12.3):(2.3.4.1)=4.5.3.3

4.

() .

, .

a:b=q, c:d=q, :

a : b = c : d

: (a:b), (c:d), (a d) (b c).

5.

:

(1)

a : b = c : d 6:3=8:4 ad = bc 6.4=3.8

10

(2) , , .

ad = bc 9.5 = 45 3.15=45 a:b=c:d 9:3=15:5

(3) : , , .

, :

a:b=c:d c:d=a:b

a:c=b:d c:a=d:b

b:d=a:c d:b=c:a

b:a=d:c d:c=b:a

(4) , .

6:3=4:2

(6.6):3 = (4.6):2 (6:2):3 = (4:2):2 36:3 = 24:2 3:3 = 2:2

(5) , .

2:4 = 1:2 4:9 = 16:36

(2

4)

2= (

1

2)

2

4

9 =

16

36

4

16 =

1

4

4

9=

16

36

4:16=1:4 2

3 =

4

6

2:3=4:6

(6) .

12:6 = 4:2

3:2 = 6:4

2:1 = 4:2

: 12.3.2 : 6.2.1 = 4.6.4 : 2.4.2

72:12 = 96:16

11

6. 6.1.

.

a : x = x : d 40 : x = x : 10

6.2.

, .

6:3=2

18:9=2

8:4=2

6:18:8 = 3:9:4

, :

A:B = 3:4

B:C = 5:10

C:D = 5:11

I. . A:B = 3:4 : A:B = 3:4

B:C = 5:10

AB:BC = 15:40

, A:C = 15:40

: A:B = 3:4

B:C = 5:10

C:D = 5:11

ABC:BCD = 75:440

BC A:D = 75:440

: A:B = 3:4

A:C = 15:40

A:D = 75:440

12

() .

A:B = 75:100

A:C = 75:200

A:D = 75:440

, .

A:B:C:D = 75:100:200:440

5 : A:B:C:D = 15:20:40:88

II. , , . A=3, =4. 3 4 C D.

B:C = 5:10 C:D = 5:11

4:C = 5:10 8:D = 5:11

= 4.10

5= 8 =

8.11

5=

88

5

:

A:B:C:D = 3:4:8: 88

5

, 5 : A:B:C:D = 15:20:40:440

13

. 1

1:

1. . 2. . 3. .

(1) .

10:5=2

10.2:5.2=20:10=2

10/5:5/5=2:1=2

(2) .

16:2=8

32:4=8

(3) , .

12:3=4

6:2=3

: (12.6):(3.2)=4.3 72:6=12

15

. 2

1:

1. . 2. .

(1)

4:2=8:4

4.4=2.8

16=16

(2) , , .

12.3=36 6.6=36 12:6=6:3

2=2

(3) : , , .

10:2=15:3 15:3=10:2

10:15=2:3 15:10=3:2

2:3=10:15 3:2=15:10

2:10=3:15 3:15=2:10

(4) , .

24:12=10:5 (24.2):12=(10.2):5 (24:2):12=(10:2):5

2=2 48:12=20:5 12:12=5:5

4=4 1=1

(5) , .

10:2 = 5:1 9:4 = 36:16

16

(10

2)

2= (

5

1)

2

9

4=

36

16

100

4 =

25

1

3

2 =

6

4

100:4=25:1 3:2=6:4

(6) .

24:12 = 8:4

9:6 = 18:12

10:5 = 20:10

: 24.9.10 : 12.6.5 = 8.18.20 : 4.12.10

2160:360 = 2880:480

6:1=6:1

3. .

17

II :

1. 2.

2.1. 2.2.

3. 4.

, :

o ; o ; o ; o ; o ; o .

18

1.

, .

.

2. 2.1.

(), .

2.2.

(), .

* () .

1: 27200 . . , 20 ., 32 . 40 .

x, y z, :

x:y:z = 20:32:40

, 4 : x:y:z = 5:8:10

:

(x+y+z):(5+8+10) = x:5

(x+y+z):(5+8+10) = y:8

(x+y+z):(5+8+10) = z:10

x+y+z = 27200, x, y, z : 27200: (5+8+10)

19

27200:23 = x:5 = 27200

23 . 5 = 5913 .

27200:23 = y:8 = 27200

23 . 8 = 9461 .

27200:23 = z:10 = 27200

23 . 10 = 11826 .

20 . 5913 ., 32 . 9461 ., 40 . 11826 .

2: 27200 . . , 20 ., 32 . 40 .

x:y:z = 1

20

1

32

1

40

, 160 x:y:z = 8:5:4

: (x+y+z):(8+5+4) = x:8

(x+y+z):(8+5+4) = y:5

(x+y+z):(8+5+4) = z:4

x+y+z = 27200, x, y, z : 27200: (8+5+4)

27200:17 = x:8 = 27200

17 . 8 = 12800 .

27200:17 = y:5 = 27200

17 . 5 = 8000 .

27200:17 = z:4 = 27200

17 . 4 = 6400 .

20 . 12800 ., 32 . 8000 ., 40 . 6400 .

3: 400000 . , 3 4 ; 5 3 D 1 4 . ? , , :

A:B = 3:4

B:C = 5:3

D:C = 1:4

20

, :`

A:B:C:D = 3:4: 12

5

3

5

, 5 : A:B:C:D = 15:20:12:3

: (A+B+C+D):(15+20+12+3) = A:15

(A+B+C+D):(15+20+12+3) = B:20

(A+B+C+D):(15+20+12+3) = C:12

(A+B+C+D):(15+20+12+3) = D:3

A+B+C+D .. 400000 ., (15+20+12+3) = 50 :

400000:50 = :15 = 400000

50 . 15 = 120000 .

400000:50 = :20 = 400000

50 . 20 = 160000 .

400000:50 = C:12 C= 400000

50 . 12 = 96000 .

400000:50 = D:3 = 400000

50 . 3 = 24000 .

120000 ., 160000 ., C 96000 . D 24000 .

4: , C catering 216000 . , . : - 2880 , 150 - 3200 , 100 - 3840 , 60 . ?

: A+B+C = 216000

: A:B:C = 2880:3200:3840

21

A:B:C = 1

150

1

100

1

60

,

A:B:C = 2880

150

3200

100

3840

60

, : A:B:C = 3:5:10

: (A+B+C):(3+5+10) = A:3

(A+B+C):(3+5+10) = :5 (A+B+C):(3+5+10) = :10

A+B+C .. 216000 ., (3+5+10) = 18 :

216000:18 = :3 = 216000

18 . 3 = 36000 .

216000:18 = :5 = 216000

18 . 5 = 60000 .

216000:18 = :10 = 216000

18 . 10 = 120000 .

36000 ., 60000 ., C 120000 .

3.

, , , , . , .

, , .

.

4.

, :

22

(1) , . , ;

(2) ;

(3) , ;

(4) .

1: 60 . , 80 . 640 ?

, , :

. = 60 . 80 . = 640 .

, () , :

60 80 640

: 80 = 60.640

= 60.640

80= 480

60 . 480 .

2: 1360,8 . 8 1 . , 1 = 39,65 .?

: =1360,8; 8p=1lb; 1lb=453,6; 1000=1; 1=39,65 ; 1=100p.

23

, , , :

= 1360,8 1 = 1000 453,6 = 1lb 1lb = 8p

100p = 1 1 =39,65

, , :

1360,8 1 1000

453,6 1lb 1lb 8p

100p 1 1 39,65

= 1360,8.1000.1.8.1.39,65

1.453,6.1.100.1= 9516 .

9516 .

3: 100ya 9 . , . ?

1 1 60 1 60 9 100ya 1ya 0,914 m

1000 m 1 km

= 1.60.60.100.0,914.1

1.1.9.1.1000= 36,56 .

36,56 .

24

4: 10 . , 1$=47 .

1 1 1000 453,6 1 1 10

100 1 $ 1$ 47

= 1.1000.1.10.1.47

1.453,6.1.100= 10 .

1 . 10 .

25

. 3

2:

1) , 2373000 . , 1/6 , 2/5 3/8 . ? (: =420000 , =1008000 , =945000 )

2) 5550 lunch-, : 10 , 12 8 . , lunch- ? (: =1800, =1500, =2250)

3) 87000 . . , : A:B=4:3 C:B=6:2. ? (: =21750 , =16312,5 ., =48937,5 .)

4) 63800 . . - 3600, 20 - 2800, 25 - 2000, 15 . ? (: = 27000, = 16800, = 20000)

27

. 4

3:

1) 2,5 . 1 , 1 70 . (: 190 1 )

2) 80 , 120 1700 .? (: 1 = 14 .; 80 = 1133 .)

3) 12 30 . 1 = 61,5 .? (: 1 154 .)

4) 345 . 615 . . , 1 . 650 ., 720 . , 1700 .? (: 287 .)

5) 12 . 8 ? ? (: 192 8 ; 1 = 2,5 .)

29

III :

1. 1.1. 1.2. 1.3. 1.4. 1.5.

, :

o ; o

; o .

30

1.

, : , , , . .

, () () . .

.

1.1.

: . ()

. .

(, , .) .

=1+2+3++

=

=1

n , i=1,2,3,,n

:

(1) ;

(2) ;

(3) .

1: , : 240, 215, 260, 255, 230 300 . ?

=

=1

=

1+2+3+4+5+6

=

240+215+260+255+230+300

6 = 250

31

, (, , ) . () (f) .

= 11+22+33+

1+ 2+3++ =

=1

=1

, .

2: , :

400 . 60 . 1 . 300 . 50 . 1 . 500 . 40 . 1 . 800 . 70 . 1 .

1 . .

11+22+33+

1+ 2+3++ =

60.400+50.300+40.500+70.800

400+300+500+800 = 57,5 .

1.2.

: . n-

. , . . , , . .

32

:

= 1. 2. 3..

3: , : 500, 600, 720, 864 1037. ?

= 1. 2. 3..

= 500.600.720.864.10375

= 720

. :

= 11 . 2

2 . 33 .

: n =

=1

1.3.

(. .).

.

, .

: (1) ,

; (2)

.

: .

:

=

1

1+

1

2+

1

3++

1

=

1

=1

33

4: . 20 ., 30 ., 40 . 60 . ?

=

1

1+

1

2+

1

3++

1

=

41

20+

1

30+

1

40+

1

60

= 30 .

:

= 1+2+3+ +

11

+22

+33

++

=

=1

n= =1

5: 1- 60- . 30/, 61- 340- . 40/, 341- 441- . 50 /. , ?

= 1+2+3+ +

11

+22

+33

++

1 = 1-60 = 60 2=61-340 = 180 3 = 341-441 = 100 1 = 30 2 = 40 3 = 50

= 60+180+10060

30+

180

40+

100

50 = 40 /

1.4.

() , . :

= +1

2

, . , , .

34

1.5.

() , .

6: , 21 , , :

03/01 - 52 10/01 - 51 17/01 - 46 24/01 - 55 04/01 - 36 11/01 - 54 18/01 - 51 25/01 - 57

05/01 - 45 12/01 - 48 19/01 - 57 26/01 - 50

06/01 - 54 13/01 - 50 20/01 - 63 27/01 - 56

07/01 - 69 14/01 - 49 21/01 - 54 28/01 - 47

31/01 - 48

36 45 46 47 48 49 50 51 52 54 55 56 57 63 69

48 50 51 54 57

54

21 . , 51 , 51 10 .

54 ( ) 54 .

35

. 5 3:

1) , , : 240, 215, 260, 255, 230, 226 300. ? (: 247 )

2) , : - 100 . 45 . 1 . - 100 . 35 . 1 . - 100 . 60 . 1 . - 100 . 25 . 1 .

1 . . (: 41 .)

3) , : 12, 10, 9, 11, 10 14 . ? (: 11 )

37

. 6

3: ,

1) . 20 ., 30 ., 40 . ? (: 28 .)

2) 9-12 10 , 12-16 20 , 16-21 30 . , ? (: 15 )

3) , : 3- 32; 10- 31; 17- 46; 24- 35 4- 36; 11- 44; 18- 31; 25- 44 6- 44 ; 13- 40; 20- 33; 27- 46 31- 38

(: =38, =44)

39

IV :

1. 2.

, :

o ; o ; o .

40

1.

, , .

: (1) ,

, . .

(2) , , . . ,

. , .

2.

, . : , . , .

1: , 48 ./. 30 ./., 360 . , 40 ./. ?

48x + 30y = 40(x+y)

48x + 30y = 40x + 40y

48x-40x = 40y-30y

x(48-40) = y(40-30)

x:y = (40-30):(48-40)

41

x:y = 10:8 : x+y=360 (x+y):(10+8) = x:10

(x+y):(10+8) = y:8

360:18=x:10 x=360.10/18 = 200 . 360:18=y:8 y=360.8/18=160 .

360 . 40 ./., 200 . 48 ./. 160 . 30 ./.

* : 48 (40-30) = 10

40

30 (48-40) = 8

10, (40-30) 8, (48-40) . (360 .) (10+8=18), . . , . .

360:18=20

20.10 ( ) = 200 . 20.8 ( ) = 160 .

2: 40 ./., 44 ./. 50 ./. 480 . 45 ./. ?

40x+44y+50z = 45(x+y+z)

40x+44y+50z = 45x+45y+45z

5z=5x+y x=y 5z=6y

z:y=6:5

z:x=6:5

x:y:z=5:5:6 : x+y+z=480 (x+y+z):(5+5+6)=x:5

(x+y+z):(5+5+6)=y:5

(x+y+z):(5+5+6)=z:6

480:16=x:5 x=480.5/16 x=150 . 480:16=y:5 y=480.5/16 y=150 . 480:16=z:6 z=480.6/16 z=180 .

42

480 . 45 ./., 150 . 40 ./., 150 . 44 ./. 180 . 50 ./.

* :

40 (50-45)=5 5.30=150 . 44 (50-45)=5 5.30=150 .

45

50 (45-44)+(45-40)=6 6.30=180 .

480:(5+5+6)

480:16=30

43

. 7 4:

1) 800, 850, 930 950 , 115 . 900 ? (: 15, 25, 50, 25)

2) 70%, 62%, 52% 40% 240 53%? ? (: : 1:13:17:9, 6, 78, 102, 54)

3) 120, 95, 92 106 . 624 . 100 ./. . ? (: : 5:8:20:6, . : 80, 128, 320, 96)

45

V :

1. 2. 3. 4. /

4.1. / / 4.2. / / 4.3. / /

, :

o , ; o

; o

.

46

1.

, / , .

100 .

2.

1000 .

3.

100 . %. .

1000 . . .

. .

, . .

(/), .

4. /

, :

(1) () (2) (+) (3) (-)

47

, , , / .

4.1. / /

/ , / /.

: 100

, :

:=100: , :

:=1000:

4.2. / /

/ , / /. / / .

: :=100:

(+):(100+)=:100 (+):(100+)=:

: :=1000:

(+):(1000+)=:1000 (+):(1000+)=:

48

4.3. / /

/ , / /.

: :=100:

(-):(100-)=:100 (-):(100-)=:

: :=1000:

(-):(1000-)=:1000 (-):(1000-)=:

1: 2000 . 5%. ?

: *

=2000, =5, =? :=100:

=.

100=

2000.5

100=

10000

100= 100 .

*

. 2000 . 100 . 5 .

= 2000.5

100=

10000

100= 100 .

2: 20% 2000 . , ?

* :

=?, =20, =2000 :=100:

49

=.100

=

2000.100

20=

200000

20= 10000

= +

= 10000+2000 = 12000

* :

=?, =20, =2000

(+):(100+) = :100, = .100

(+2000):(100+20)= 2000.100

20 : 100

(+2000):120 = 10000:100 100(+2000) = 10000.120 100+200000 = 1200000

100 = 1000000 =10000

+ =

10000+2000=12000

*

2000 20% 100

= 2000.100

20=

200000

20= 10000

10000 +2000 = 12000

3: , 400, 600, 800, 900 1200 15%. .

* ,

1-

100

50

1- 15

100= 1 0,15 = 0,85

, : 400 . 0,85 = 340 600 . 0,85 = 510 800 . 0,85 = 680 900 . 0,85 = 765 1200.0,85 = 1020

4: , 25%. , 400, 600, 800, 900 1200 . .

* ,

1+

100

1+ 25

100= 1 + 0,25 = 1,25

, : 400 . 1,25 = 500 600 . 1,25 = 750 800 . 1,25 = 1000 900 . 1,25 = 1125 1200.1,25 = 1500

51

. 8

5:

1) , , 2400 . , 25%. ? (: 600 . 1800 .)

2) . , 8%, 4%. , : - 80 ., 110 ., 70 ., 100 . 60 . (: - 77 ., 119 ., 67 ., 108 . 58 .)

3) 20%, 200 . , ? (: 1000 , 800 )

4) 15% 92 . . ? (: 80 ., 12 . )

5) 8%, , 5% 483 . ? (: 8% 500 ; 5% 460 )

53

VI :

1. 2. 3.

3.1. 3.2. 3.3.

, :

o ; o ; o ; o

.

54

1.

index , . (, , , .).

, : (1) -

100 ( ) .

(2) - . 100

( ) ( ).

100 ( ) ( ).

1: : 2007 . 250 .; 2008 . 280 .; 2009 . 310 .; 2010 . 360 . 2011 . 330 . .

) (2007 )

280 310 360 330 250 100 250 100 250 100 250 100

=280.100

250= 112 =

310.100

250= 124 =

360.100

250= 144 =

330.100

250= 132

112 280 . 2008 . 12% 250 . 2007 . .

) 280 310 360 330 250 100 280 100 310 100 360 100

=280.100

250= 112 =

310.100

280= 111 =

360.100

310= 116 =

330.100

360= 92

92 330 . 2011 . 8% (100-92) 360 . 2010 . .

55

2.

, . . 100 , . ( ), . , , . (g), (m) (d). , 30 , , 365 360 . Va. (30;360); (30;365); (;360); (;365), , . .

3.

, , :

(1) ; (2) (3) .

:

S - S+i - S-i - p - t - (g), (m)

(d)

56

3.1.

, .

: S:i = 100:p.g ( )

S:i = 1200:p.m ( ) S:i = 36000:p.d ( 360 ) S:i = 36500:p.d ( 365 )

2: 50000. 3 ., 8%. ?

S=50000, p=8, g=3, i=?

, S:i = 100:p.g, i=..

100 =

50000.8.3

100 = 12000 .

3: 60000 . 6 20 , 6%, ?

S=60000, p=6, d=200 (6.30+20), i=?

, S:i = 36000:p.d, i=..

36000 =

60000.6.200

36000 = 2000 .

3.2.

, .

:

(S+i):(100+p.g)=S:100 ( ) (S+i):(100+p.g)=i:p.g

(S+i):(1200+p.m)=S:1200 ( ) (S+i):(1200+p.m)=i:p.m

(S+i):(36000+p.d)=S:36000 ( 360 )

(S+i):(36000+p.d)=i:p.d

57

(S+i):(36500+p.d)=S:36500 ( 365 )

(S+i):(36500+p.d)=i:p.d

4: 6% , 240 , 62400 . , ?

S+i=62400, p=6, d=240, S=? i=?

, (S+i):(36000+p.d)=S:36000

S=(+).36000

36000+.=

62400.36000

36000+6.240 = 60000 .

S+i=62400, i=62400-S, i=62400-60000=2400 .

3.3.

, .

:

(S-i):(100-p.g)=S:100 ( ) (S-i):(100-p.g)=i:p.g

(S-i):(1200-p.m)=S:1200 ( ) (S-i):(1200-p.m)=i:p.m

(S-i):(36000-p.d)=S:36000 ( 360 )

(S-i):(36000-p.d)=i:p.d

(S-i):(36500-p.d)=S:36500 ( 365 )

(S-i):(36500-p.d)=i:p.d

58

5: 6% , 8 , 60000 . ja ?

S-i=60000, p=6, m=8, i=?

, (S-i):(1200-p.m)=i:p.m

i=()..

1200.=

60000.6.8

12006.8 = 2500 .

2500 .

59

. 9 6:

1) e , : 2007 . 20000 .; 2008 . 22000 .; 2009 . 31000 .; 2010 . 33600 . 2011 . 33000 . ( 2007) . (: : 110, 155, 167, 165; : 110, 141, 108, 98)

2) 40000 . 8 , 6%, ? (: 1600 .)

3) 30000 . 4% 3000 . . ? (: 2 . 6 )

4) 360 , 20% , 90000 . , ? (: S=75000 ., i=15000 .)

5) 7 , 120000 . 10% . ? (: 7434 .)

61

VII :

1. 2. 3.

3.1. 3.2.

3.3. 3.3.1. () 3.3.2. 3.3.3.

3.3.4.

, :

o ;

o ; o .

62

1.

calculus, . , , , .

, . , , , .

2.

, :

(1) ; (2) ; (3) ; (4) , (5) ; (6) (7) .

3.

, :

(1) ; (2) (3)

3.1.

, . : , , , .

63

3.2.

, : (1) () -

(2) () -

, .

3.3.

, : (1) () -

; (2) - ; (3) (4) .

3.3.1. ()

, . :

(1) - , /. , /.

(2) - /. , , . . , , .

1) 5000 , 200000 . .

64

1 2 3 4

5000 2000000 400

( 4) ( 3) ( 2).

2) 1200 :

- 350 ; - 400 - 450 .

, ( ) 5280000 . : 1,6:1:0,8. .

-

. .

. 1 .

.

1 2 3 4 5 6 7

350 1,6 560 4000 2240000 6400

400 1 400 4000 1600000 4000

+ 450 0,8 360 4000 1440000 3200

( 1) : 1,6:1:0,8 ( 3). ( 2) ( 4). (5280000 .) ( 4: 560+400+360=1320). 4000 . ( 5). , ( 4) ( 5), ( 6). ( 6) ( ) ( 2), ( 7).

65

, : 6400 ., 4000 . 3200 .

3.3.2.

, / / . . . /.

3) : , . , :

- 1500 ; - 1200 - 1800 .

, , :

80000 150000 40000

60000 120000 25000

100000 180000 60000

: 240000 450000 125000

, 120000 . :

- 72000 . - 48000 . - . ,

.

, ,

: .100

.

: -

72000 .100

240000 = 30%

66

- -

48000 .100

240000 = 20%.

, ( ) :

= 80000 .30

100 = 24000 .

= 60000 .30

100 = 18000 .

= 100000 .30

100 = 30000 .

, - :

= 80000 .20

100 = 16000 .

= 60000 .20

100 = 12000 .

= 100000 .20

100 = 20000 .

- , .

1. 2. 3. 4. 5. -

240000

450000

125000

72000

48000

80000

150000

40000

24000

16000

60000

120000

25000

18000

12000

100000

180000

60000

30000

20000

: 935000 310000 235000 390000

1500 1200 1800

207 196 217

. , : - 207 ., - 196 . - 217 .

67

3.3.3.

. , . , . . , /, /.

4) T 40000 ., 35 . , , , 5000 . .

1 2 3 4 5

35 40000 35000 1000

( 1). , , 40000 . ( 3). 5000 . - , 35000 . ( 4). , - 35 , 1000 . ( 5).

3.3.4.

.

68

( : + ), () . , .

, . , , .

, , :

1. 2.

a. b. c.

3. ( , , .)

4. ( ) a. b.

5. (/)

5) 5000 , 1200 . . , .

: 1. 1250000 2. 2000000 3. 500000 4. 250000 5. 400000 6. 700000

: 5100000

, , (),

69

. , : 1, 2, 4 5, : 3 6.

() 1. 1250000 2. 2000000 3. 250000 4. 400000 : 3900000

1. 500000 2. 700000 : 1200000

, . , ..:

= 5000 . 1200 = 6000000 .

, :

(1) 6000000 (2) - 3900000 (3) (1-2) 2100000 (4) - 1200000 (5) (3-4) 900000 .

900000 .

71

. 10 7:

1) 8000 , 10000000 . . (: 1250 .)

2) , . , , 400 , 1000000 . . (: 2500 .)

3) 300 : - 50 ; - 160 - 90 .

, ( ) 1000000 . : 1,6:1,2:1. . (: =4416 ., =3312 . =2760 .)

4) 200 , :

- 150 ; - 15 - 35 .

, ( ) 120000 . : 1,5:1:0,7. . (: =675, =450 =320)

73

. 11 7: ,

1) , : , . , : 15000 , 2000 1000 . , 150000 . , :

25000 30000 5000

15000 20000 5000

20000 25000 5000

50000 . : 30000 . , 20000 . - . . (: : 5 ., 26 ., 67 .)

2) , : , . , : 100 , 70 120 . , 75000 . , :

12000 13000 2000

10000 11000 2000

13000 10000 2000

25000 . : 15000 . , 10000 . - . . (: =355 ., =430 . =280 .)

74

3) 7000 ., 5 . , , , 1500 . . (: =1100 .)

4) 9200 ., 5 . , , , 1800 . . (: =1480 .)

5) 25000 , 1500 . . , direct costing .

1. 3250000 2. 7000000 3. 900000 4. 450000 5. 800000 6. 1500000

(: =23600000 .)

75

. 12

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