VI-J NOTES Ex-8.3

VI-J NOTES Ex-8.3

1. Are 12, 8,8,12 in proportion?

Ans. Product of extreme terms=12x12

                                                 =144

Product of middle terms          =18x8

                                                 =144

Therefore, they are in proportion.

2. Determine if the following are in proportion.

(i) 30,45,16,24

Ans. Product of extreme terms=30x24

                                                 =720

Product of middle terms          =45x16

                                                 =720

Therefore, they are in proportion.

(ii) 6,10,18,35

Ans. Product of extreme terms=6x35

                                                 =210

Product of middle terms          =10x18

                                                 =180

Therefore, they are not in proportion.

(iii) 33, 44, 75,100

Ans. Product of extreme terms=33x100

                                                 =3300

Product of middle terms          =44x75

                                                 =3300

Therefore, they are in proportion.

(iv) 30, 40, 40, 55

Ans. Product of extreme terms=30x55

                                                 =1650

Product of middle terms          =40x40

                                                 =1600

Therefore, they are not in proportion.

(V) 25 30 40 48

Ans. Product of extreme terms=25x48

                                                 =1200

Product of middle terms          =30x40

                                                =1200

(We) 91,104,119,136

Ans. Product of extreme terms=91x136

                                                 =12376

Product of middle terms          =104x119

                                                 =12376

Therefore, they are in proportion.

3. Verify whether the following numbers are in proportion.

(i) 21,16,35,10

Ans. Product of extreme terms=21x10

                                                 =210

Product of middle terms          =16x35

                                                 =560

Therefore, they are not in proportion.

(ii) 24, 45, 16, 30

Ans. Product of extreme terms=24x30

                                                 =720

Product of middle terms          =45x16

                                                 =720

Therefore, they are in proportion.

4. If the first three terms of a proportion are 9,8 and 54 respectively, find the fourth term.

Ans. Let fourth term be a

9:8:: 54: a

9xa = 8x54

a    =8x54

           9

     = 48                                            

5. If the first, second and fourth terms of a proportion are3,11 and 55, find the third term

Ans. Let third term be a.

3:11:: a:55

11xa = 3x55

a     =3x55

            11

      =15

6. Find the value of p in each case.

(i) 9: p :: 54:48

Years. 9x8 = px54

p            = 9x48

                 54

              =8

(Ii) 55:11 :: p 3

Years. 11xp = 55x3

         p     =55x3

             11

      =15

(Iii) p: 8 :: 10:16

Years. Px16 = 8x10

p              =8x10

                    16

                =5

(Iv) 10: 16-20: p

Years. 10xp = 16x20

p           =16x20

                   10

            =32

7. Show that 25, 35, 49 are in continued proportion.

Ans. (a, b, c are continued proportion if b x b = a x c)

a = 25, b = 35, c = 49

Bxb = 35x35 = 1225

a x c = 49x25 = 1225

Therefore, b x b = a x c = 1225

8. Find the mean proportion of 3 and 12.

Years. 3: P:: P: 12

Prime factors of 3 = 3

Prime factors of 12 = 3x2x2

                               = 3x2

                               = 6

Therefore, 3: 6 :: 6:12

9. Find the mean proportion of 48 and 75.

48: P :: P: 75

Prime factors of 48 = 2x2x2x2x3

Prime factors of 75 = 5x5x3

                               = 2x2x3x5

                              = 60

Therefore, 48:60:: 60:75

10. The ratio of the length of school playground to its width is 5:3. If the width of the ground is 66 meters, find the length of the playground.

Ans. Length: Breadth = 5:3

Breadth               =66m

Let length be      = 5x

Let Breadth be   = 3x

                    x    = 66

                              3

                                  = 22      

       Length               = 5x22

                                 = 110 m

11. The ratio of the income to the expenditure of a family is 9:4. Find the income if the saving is Rupees 3600.

Ans. Income: Expenditure= 9:4

        Income                      = 9x

        Expenditure              = 4x

        Saving                      = 9x-4x

                                         = 5x

                                         = Rupees 3600

       5x = 3600

       x                                = 3600

                                               5

                                = 720

Income                 = 9x720

                             = Rupees 6480

12. Arrange the following numbers in the correct order to make them in proportion. The first number has to be the first term of the proportion.

(i). 8, 24, 9, 27

Years. 8 x 3, 9 x 3

        Therefore, 8:24::9:27

(ii). 0.9, 10, 4, 0.36

Years. 0.9x4, 0.36x10

Therefore, 0.9:0.36::10:4

(iii). 8, 40, 200, 40

Years. 8x5, 40x5

         Therefore, 8:40::40:200

(iv) 5, 90,15, 30

Years. 5x3.30x3

        Therefore, 5:15::30:90

13. Do the ratio of 12 cm to 3m and 8 seconds to 3 minutes form a proportion?

Years. 12cm: 3m

        1m             = 100 cm

        3m = 300cm

      12:300

      LCM of 12 and 300= 1:25

      8 seconds: 3 minutes

      1 minute= 60 seconds

      3minutes= 3x60 seconds

                     = 180 seconds

      LCM of 8 and 180=2:45

14. Find the mean proportion of the following

(i). 81,121

Years. 81: b :: b: 121

         bxb = 81x121

         Prime factors of 81 and 121= 3x3x3x311x11

                                                     = 3x3x11  

                                                     = 99  

        Therefore, 81:99::99:121

(ii). 100,256

Years. 100: b :: b: 256

           Bxb = 100x256

         Prime factors of 100 and 256=5x5x2x2x2x2x2x2x2x2x2x2

                                                        = 5x2x2x2x2x2

                                                        = 160

      Therefore, 100:160::160:256       

(iii). 9,81

Years. 9: b :: b: 81

        bxb = 9x81

        Prime factors of 9 and 81= 3x3x3x3x3x3

                                                 = 3x3x3

                                                 = 27

       Therefore, 9:27::27:81

15. If 15 books cost Rupees 180, what is the cost of 12 books?

Ans. Cost of 15 Books= Rupees 180

        Cost of 1 Book    = 180

                                15

                                    = Rupees 12

       Therefore, the cost of

        12 books             = 12x12

                                    =