NCERT Grade 8-Direct and Inverse Proportions-Answers

NCERT Solutions for Class 8 Maths

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1.    Charges per hour:

Here, the charges per hour are not same, i.e., C1 ≠ C2 ≠ C3 ≠ C4

Therefore, the parking charges are not in direct proportion to the parking time.

2.    Let the ratio of parts of red pigment and parts of base be 

3.    Let the parts of red pigment mix with 1800 mL base be x.

Since it is in direct proportion.

Hence with base 1800 mL, 24 parts red pigment should be mixed.

4.   Let the number of bottles filled in five hours be x.

Hours     1                   x

Bottles   75             1800

Hence ratio of hours and bottles are in direct proportion.

Hence machine will fill 700 bottles in five hours.

5.    Let enlarged length of bacteria be x.

Actual length of bacteria  cm = = 10-4 cm

Length                          5                    x

Enlarged length    50,000      20,000

Here length and enlarged of bacteria are in direct proportion.

Hence the enlarged length of bacteria is 2 cm.

6.    Let the length of model ship be x.

Length of actual ship (in m)        12           28

Length of model ship (in cm)      9              x

Here length of mast and actual length of ship are in direct proportion.

Hence length of the model ship is 21 cm.

7.    (i) Let sugar crystals be x.

Weight of sugar (in kg)         2                 5

No. of crystals                        9 × 106            x

Here weight of sugar and number of crystals are in direct proportion.

Hence the number of sugar crystals is 2.25 × 107.

(ii) Let sugar crystal be x.

Weight of sugar (in kg)           2              1.2

No. of crystals                           9 × 106        x

Here weight of sugar and number of crystals are in direct proportion.

Hence the number of sugar crystals is 5.4 × 106.

8.    Let distance covered in the map be x.

Actual distance (in km)                         18        72

Distance covered in map (in cm)        1          x

Here actual distance and distance covered in the map are in direct proportion.

Hence distance covered in the map is 4 cm.

9.   Here height of the pole and length of the shadow are in direct proportion.

And 1 m = 100 cm

5m 60 cm = 5 × 100 + 60 = 560 cm

3 m 20 cm = 3 × 100 + 20 = 320 cm

10 m 50 cm = 10 × 100 + 50 = 1050 cm

5 m= 5 × 100 = 500 cm

(i) Let the length of the shadow of another pole be x.

Height of pole (in cm)                560             1050

Length of shadow (in cm)         320               x

Hence length of the shadow of another pole is 6 cm.

(ii) Let the height of the pole be x.

Height of pole (in cm)              560         x

Length of shadow (in cm)       320       500

Hence height of the pole is 8 m 75 cm.

10.  Let distance covered in 5 hours be x km.

∵ 1 hour = 60 minutes

∴ 5 hour = 5 × 60 = 300 minutes.

Distance (in km)         14      x

Time (in minutes)      25    300

Here distance covered and time in direct proportion.

Hence the distance covered in 5 hours is 168 km.

11.  (i) The number of workers and the time to complete the job is in inverse proportion because less workers will take more time to complete a work and more workers will take less time to complete the same work.

(ii) Time and distance covered in direct proportion.

(iii) It is a direct proportion because more are of cultivated land will yield more crops.

(iv) Time and speed are inverse proportion because if time is less, speed is more.

(v) It is a inverse proportion. If the population of a country increases, the area of land per person decreases.

12.  Here number of winners and prize money are in inverse proportion because winners are increasing, prize money is decreasing.

When the number of winners are 4, each winner will get 

When the number of winners are 5, each winner will get = 

When the number of winners are 8, each winner will get 

When the number of winners are 10, each winner will get 

When the number of winners are 20, each winner will get 

13.  Here the number of spokes are increasing and the angle between a pair of consecutive spokes is decreasing. So, it is a inverse proportion and angle at the centre of a circle is 360°.

When the number of spokes is 8, then angle between a pair of consecutive spokes 

When the number of spokes is 10, then angle between a pair of consecutive spokes 

When the number of spokes is 12, then angle between a pair of consecutive spokes 

No. of spokes                                                                    4          6        8       10     12

Angle between a pair of consecutive spokes       90°     60°     45°    36°   30°

(i) Yes, the number of spokes and the angles formed between a pair of consecutive spokes is in inverse proportion.

(ii) When the number of spokes is 15, then angle between a pair of consecutive spokes 

14.  ∵ Each child gets = 5 sweets

∴ 24 children will get 24 × 5 = 120 sweets

Total number of sweets = 120

If the number of children is reduced by 4, then children left = 24 – 4 = 20

Now each child will get sweets  6 sweers

15.  Let the number of days be x.

Total number of animals = 20 + 10 = 30

Animals   20           30

Days           6              x

Here the number of animals and the number of days are in inverse proportion.

Hence the food will last for four days.

16.  Let time take to complete the job be x.

Persons   3              4

Days          4              x

Here the number of persons and the number of days are in inverse proportion.

Hence they will complete the job in 3 days.

17.  Let the number of boxes be x.

No. of bottles in each box             12           20

Boxes                                                      25           x

Here the number of bottles and the number of boxes are in inverse proportion.

Hence 15 boxes would be filled.

18.  Let the number of machines required be x.

Days                      63           54

Machines            42           x

Here the number of machines and the number of days are in inverse proportion.

Hence 49 machines would be required.

19.  Let the number of hours be x.

Speed (in km/hr)              60           80

Time (in hours)                  2              x

Here the speed of car and time are in inverse proportion.

Hence the car will take  hours to reach its destination.

20.  (i) Let the number of days be x.

Persons   2              1

Days         3              x

Here the number of persons and the number of days are in inverse proportion.

(ii) Let the number of persons be c.

Persons   2              x

Days          3              1

Here the number of persons and the number of days are in inverse proportion.

21.  Let the duration of each period be x.

Period                                                         8              9

Duration of period (in minutes)   45           x

Here the number periods and the duration of periods are in inverse proportion

Hence duration of each period would be 40 minutes.

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