NCERT Solution for Direct and Inverse Proportions

Check if the parking charges are in direct proportion to the parking time.

∴ The parking charges are not in direct proportion to the parking time.

So, x and y are in direct variation with the constant of variation equal to . This means that x is of y and y is eight times of x. Thus, the required entries are

The given infonrutlon in the form of a table is as follows.

The parts of red pigment and the parts of base are in direct proportion. Therefore, we obtain

Thus, 24 parts of red pigments shook! be mixed with 1800 mL of base.

The given information in the form of a table is as follows.

The number of bottles and the time taken to fill these bottles are in direct proportion.

Therefore, we obtain

Thus 700 bottles wtll be filled in 5 hours.

What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, wnat would be its enlarged length?

Suppose x be the enlarged length of the bacteria when its photograph is enlarged 20000 times.

Then the information can be put in the following tabular form:

Hence, its enlarged length is 2 cm.

We know that the dimensions of the actual ship and the model ship are directly proportional to each other.

Thus, the length of the model ship is 21 cm.

The distances covered on road and represented on map are directly proportional to each other.

Therefore, we obtain

Hence, the distance represented on the map is 4 cm.

Then, the given information can be exhibited in the following tabular form:

be x km.

We know,1 hour = 60 minutes

∴ 5 hours = (5 × 60) minutes = 300 minutes

The given information in the form of a table is as follows.

The distance travelled by the truck and the time taken the truck are directly proportional to each by other. Therefore,

Hence, the distance travelled by the truck is 168 km.

(i) The number of workers on a job and the time to complete the job.

(ii) The time taken for a journey and the distance travelled in a uniform speed.

(iii) Area of cultivated land and the crop harvested.

(iv) The time taken for a fixed journey and the speed of the vehicle.

(v) The population of a country and the area of land per person.

(iii) Clearly, more is the area cultivated land, more is the crop harvested.

So, it is a case of direct proportion.

(v) Clearly, more is the population, less is the area of land per person in a country.

So, it is a case of inverse proportion.

Number of

winners

1

2

4

5

8

10

20

winners

1

2

4

5

8

10

20

Prize for each winner

(in Rs.)

1,00,000

50,000

��

��

��

��

��

(in Rs.)

1,00,000

50,000

��

��

��

��

��

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive okes on a wheel with 15 spokes.

(iii) How many spokes would be needed, if the angle between a it of consecutive spokes is 40°?

From the given table, we obtain

4 × 90° = 360° = 6 × 60°

Thus, the number of spokes and the angle between a pair of consecutive spokes are inversely proportional to each other. Therefore,

Thus, the following table is obtained.

(i) Yes, the number of spokes and the angles formed between the pairs of consecutive spokes are in inverse proportion.

(ii) Let the angle between a pair of consecutive spokes on a wheel with 15 spokes be x. Therefore, 4 × 90° = 15 × x

Hence, the angle between a pair of consecutive spokes of a wheel, which has 15 spokes in it, is 24°.

(iii) Let the number of spokes in a wheel, which has 40° angles between a pair of consecutive spokes, be y, Therefore,

4 × 90° = y × 40°

Hence, the number of spokes in such a wheel is 9.

Let the number of sweets which each of the 20

students will get, be x.

The following table is obtained.

If the number of students is lesser, then each student will get more number of sweets.

Since this is a case of inverse proportion,

24 × 5 = 20 × x

Hence, each sent will get 6 sweets.

Clearly, more is the number of animals, less will be the number of days for food to last.

So, it is a case inverse proportion.

Hence, the food will now last for 4 days.

According to question

Since the given problem is in inverse proportion.

4 × 3 = x × 4

∴ 4 persons will take 3 days to complete the job.

Clearly, more is the number of bottles, will be the number of boxes needed for packing.

So, it is a case of inverse proportion.

Hence, the boxes needed for packing is 15.

According to question

Since number of days are decreasing number of machines must be increasing.

∴ The problem is in inverse proportion

Thus, number of machines would be required to produce the same number of articles in 54 days

= 49.

Clearly, more the speed, less will be the time taken. So, it is a case of inverse proportion.

(i) One of the persons fell Ill before the work started. How long would the job take now?

(ii) How many persons would be needed to fit the windows in one day?

Lesser the number of persons, more will be the number of days required to fit all the windows

Hence, this is a case of inverse proportion. Therefore,

2 × 3 = 1 × x

x = 6

Hence, the number of days taken by 1 man to fit all the windows is 6.

(ii) Let the number of persons required to fit all the windows in one day be y. The following table is formed.

Lesser the number of days, more will be the number of person required to fit all the windows.

Hence, this is a case of inverse proportion.

Therefore, 2 × 3 = y × 1

y = 6

Hence, 6 persons are required to fit all the windows in one day.

Clearly, more the periods, less will be the duration of the period.

So, it is a case of inverse proportion.

∴ 8 × 45 = 9 × x

Hence, the duration of period is 40 minutes.