HomeNCERT SOLUTIONS8th CLASSClass 8 Maths Chapter 13 Direct and Inverse Proportions Solutions

Class 8 Maths Chapter 13 Direct and Inverse Proportions Solutions

NCERT Class 8 Maths Chapter 13 Direct and Inverse Proportions Solutions

Chapter 13 Direct and Inverse Proportions Exercise 13.1

Ex 13.1 Class 8 Maths Question 1.
Following are the car parking charges near a railway station up to.
4 hours – ₹ 60
8 hours – ₹ 100
12 hours – ₹ 140
24 hours – ₹ 180
Check if the parking charges are in direct proportions to the parking time.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q1
Solution:
We have the ratio of time period and the parking charge.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q1.1
Hence the given quantities are not directly proportional.

Ex 13.1 Class 8 Maths Question 2.
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q2
Solution:
Let the number to be filled in the blanks be a, b, c and d respectively.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q2.1

Ex 13.1 Class 8 Maths Question 3.
In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
Solution:
Let the required red pigment be x part.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q3
Hence, the required amount of red pigment = 24 parts.

Ex 13.1 Class 8 Maths Question 4.
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Solution:
Let the required number of bottles be x.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q4
Hence the required number of bottles = 700.

Ex 13.1 Class 8 Maths Question 5.
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q5
Solution:
Let the actual length be x cm.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q5.1
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q5.2

Ex 13.1 Class 8 Maths Question 6.
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q6
Solution:
Let the required length of the model ship be x m.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q6.1

Ex 13.1 Class 8 Maths Question 7.
Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in
(i) 5 kg of sugar?
(ii) 1.2 kg of sugar?
Solution:
Let x be the number of sugar crystals needed.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q7
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q7.1

Ex 13.1 Class 8 Maths Question 8.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road of 72 km. What would be her distance covered in the map?
Solution:
Let the required distance be x km.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q8
Hence the distance covered in the map = 4 cm.

Ex 13.1 Class 8 Maths Question 9.
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time
(i) the length of the shadow cast by another pole 10 m 50 cm high,
(ii) the height of a pole which casts a shadow 5 m long.
Solution:
(i) Let the required length of shadow be x m.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q9
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q9.1

Ex 13.1 Class 8 Maths Question 10.
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Solution:
Let the required distance be x km.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Q10
Hence the required distance = 168 km.

ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-1
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-2
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-3
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-4
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-5
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-6
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-7
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1-q-8

Chapter 13 Direct and Inverse Proportions Ex 13.2

NCERT Class 8 Maths Direct and Inverse Proportions Exercise 13.2

Ex 13.2 Class 8 Maths Question 1.
Which of the following are in inverse proportion?
(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.
Solution:
(i) As the number of workers increase, the job will take less time to complete. Hence, they are inversely proportional.
(ii) For more time, more distance to travel. Hence, they are not inversely proportional.
(iii) More area of land cultivated, more crop to harvest. Hence, they are not inversely proportional.
(iv) If speed is increased, it will take less time to complete the fixed journey. Hence, they are inversely proportional.
(v) If the population of a country increases, then the area of land per person will be decreased. Hence, they are inversely proportional.

Ex 13.2 Class 8 Maths Question 2.
In a Television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

Number of winners124581020
The prize for each winner (in ₹)1,00,00050,000

Solution:
Let, the blank spaces be denoted by a, b, c, d and e.
So, we observe that 1 × 100,000 = 2 × 50,000
⇒ 1,00,000 = 1,00,000
Hence they are inversely proportional.
2 × 50,000 = 4 × a
NCERT Solutions for Class 8 Maths Direct and Inverse Proportions Ex 13.2 Q2
NCERT Solutions for Class 8 Maths Direct and Inverse Proportions Ex 13.2 Q2.1

Number of winners124581020
The prize for each winner (in ₹)1,00,00050,00025,00020,00012,50010,0005,000

Ex 13.2 Class 8 Maths Question 3.
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
NCERT Solutions for Class 8 Maths Direct and Inverse Proportions Ex 13.2 Q3

Number of spokes4681012
The angle between a pair of consecutive spokes90°60°

(i) Are the number of spokes and the angle formed between the pairs of consecutive spokes in inverse proportion.
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
Solution:
From the above table, we observe that
4 × 90° = 6 × 60°
360° = 360°
Thus the two quantities are inversely proportional.
Let the blank spaces be denoted by a, b, and c.
4 × 90° = 8 × a
NCERT Solutions for Class 8 Maths Direct and Inverse Proportions Ex 13.2 Q3.1
Hence, the required table is

Number of spokes4681012
The angle between a pair of consecutive spokes90°60°45°36°30°

(i) Yes, they are in inverse proportion
(ii) If the number of spokes is 15, then
4 × 90° = 15 × x
x = \frac { 4\times 90 }{ 15 } = 24°
(iii) If the angle between two consecutive spokes is 40°, then
4 × 90° = y × 40°
y = \frac { 4\times 90 }{ 40 } = 9 spokes.
Thus the required number of spokes = 9.

Ex 13.2 Class 8 Maths Question 4.
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is decreased by 4?
Solution:

Number of childrenNumber of Sweets
245
(24 – 4) or 20a

We observe that on increasing the number of children, number of sweets got by each will be less. So, they are in inverse proportion.
x1y1 = x2y2
where x1 = 24, y1 = 5, x2 = 20
and y2 = a(let)
24 × 5 = 20 × a
a = 6
Hence, the required number of sweets = 6.

Ex 13.2 Class 8 Maths Question 5.
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
Solution:
If the number of animals increases, then it will take fewer days to last.
Then the two quantities are in inverse proportions.

Number of animalsNumber of days
206
(20 + 10) or 30P

Let the required number of days be p.
x1y1 = x2y2
where x1 = 20, y1 = 6, x2 = 3
and y2 = p (let)
20 × 6 = 30 × p
p = 4
Hence the required number of days = 4.

Ex 13.2 Class 8 Maths Question 6.
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
Solution:
If the number of persons is increased, it will take less number of days to complete the job.
Thus, the two quantities are in inverse proportion.

Number of personsNumber of days
34
4k

Let the required number of days be k.
x1y1 = x2y2
3 × 4 = 4 × k
k = 3 days.
Hence, the required number of days = 3.

Ex 13.2 Class 8 Maths Question 7.
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
NCERT Solutions for Class 8 Maths Direct and Inverse Proportions Ex 13.2 Q7
Solution:
If the number of bottles is increased then the required number of boxes will be decreased. Thus the two quantities are in inverse proportion.

Number of boxesNumber of bottles per box
2512
x20

Let the required number of boxes be x.
x1y1 = x2y2
25 × 12 = x × 20
x = 15
Hence, the required number of boxes = 15.

Ex 13.2 Class 8 Maths Question 8.
A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
Solution:
If the number of machines is increased then less number of days would be required to produced the same number of articles.
Thus, the two quantities are in inverse proportion.

Number of machinesNumber of days
4263
x54

Let the required number of machines be x.
x1y1 = x2y2
42 × 63 = x × 54
x = 49
Hence, the required number of machines is 49.

Ex 13.2 Class 8 Maths Question 9.
A car takes 2 hours to reach a destination by traveling at a speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
Solution:
On increasing the speed, it will take less time to travel a distance.
Thus the two quantities are in inverse proportions.

Speed in km/hTime in hour
602
80x

Let the required times be x hours.
x1y1 = x2y2
60 × 2 = 80 × x
x = \frac { 3 }{ 2 } hours = 1\frac { 1 }{ 2 } hrs.
Hence, the required time = 1\frac { 1 }{ 2 } hours.

Ex 13.2 Class 8 Maths Question 10.
Two persons could fit new windows in a house in 3 days.
(i) One of the people 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?
Solution:
On increasing the number of persons, less time will be required to complete a job.
Thus, the quantities are in inverse proportion.

Number of personsNumber of days
23
(i) 1(2 – 1)x
(ii) y1

(i) Let the required number of days be x.
x1y1 = x2y2
2 × 3 = 1 × x
x = 6
Hence, the required number of days = 6
(ii) Let the required number of persons be y.
x1y1 = x2y2
2 × 3 = y × 1
y = 6
Hence, the required number of persons = 6.

Ex 13.2 Class 8 Maths Question 11.
A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?
Solution:
On increasing the duration of periods, the number of periods will be reduced.
Thus, the two quantities are in inverse proportion.

Number of periodsDuration of periods in minutes
845
9x

Let the required duration of each period be x.
x1y1 = x2y2
8 × 45 = 9 × x
x = 40 minutes
Hence, the required duration of period = 40 minutes.

ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-1
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-2
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-3
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-4
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-5
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-6
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-7
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-8
ncert-solutions-for-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2-q-9

Extra Questions Maths Chapter 13

Extra Questions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

Direct and Inverse Proportions Class 8 Extra Questions

Question 1.
A train is moving at a uniform speed of 100 km/h. How far will it travel in 20 minutes?
Solution:
Let the distance travelled by train in 20 minutes be x km.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q1
Since the speed is uniform, the distance travelled will be directly proportional to time.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q1.1
Hence, the required distance is 33\frac { 1 }{ 3 } km.

Question 2.
Complete the table if x and y vary directly.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q2
Solution:
Let the blank spaces be filled with a, b and c.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q2.1
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q2.2
Hence, the required values are a = 7, b = 15 and c = 7.5.

Question 3.
If the cost of 20 books is ₹ 180, how much will 15 books cost?
Solution:
Let the required cost be ₹ x.
Here, the two quantities vary directly.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q3

Question 4.
If x1 = 5, y1 = 7.5, x2 = 7.5 then find y2 if x and y vary directly.
Solution:
Since x and y vary directly.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q4
Hence, the required value is 11.25.

Question 5.
If 3 kg of sugar contains 9 × 108 crystals. How many sugar crystals are there in 4 kg of sugar?
Solution:
Let the required number of crystals be x.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q5
Hence, the required number of crystals = 1.2 × 109.

Question 6.
If 15 men can do a work in 12 days, how many men will do the same work in 6 days?
Solution:
Let the required number of men be x.
Less days → more men.
Thus the two quantities are inversely proportional to each other.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q6
Hence, the required number of days = 30.

Question 7.
A train travels 112 km in 1 hour 30 minutes with a certain speed. How many kilometres it will travel in 4 hours 45 minutes with the same speed?
Solution:
Let the required distance be x km.
More distance → more time
Thus, the two quantities are directly proportional.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q7
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q7.1
Hence, the required distance = 354.6 km.

Question 8.
The scale of a map is given as 1 : 50,000. Two villages are 5 cm apart on the map. Find the actual distance between them.
Solution:
Let the map distance be x cm and actual distance be y.
1 : 50,000 = x : y
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q8
Hence, the required distance = 250 km.

Question 9.
8 pipes are required to fill a tank in 1 hr 20 min. How long will it take if only 6 pipes of the same type are used?
Solution:
Let the required time be ‘t’ hours.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q9

Question 10.
15 men can build a wall in 42 hours, how many workers will be required for the same work in 30 hours?
Solution:
Let the required number of workers be x.
The number of workers, faster will they do the work.
So, the two quantities are inversely proportional.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q10
x1y1 = x2y2
⇒ 42 × 15 = 30 × x
⇒ x = 21
Hence, the required number of men = 21

Direct and Inverse Proportions Class 8 Extra Questions Short Answer Type

Question 11.
The volume of a gas V varies inversely as the pressure P for a given mass of the gas. Fill in the blank spaces in the following table:
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q11
Solution:
Since volume and pressure are inversely proportional.
PV = K
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q11.1
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q11.2
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q11.3

Question 12.
The cost of 5 metres of cloth is ₹ 210. Tabulate the cost of 2, 4, 10 and 13 metres of cloth of the same type.
Solution:
Let the length of the cloth be x m and its cost be ₹ y. We have the following table.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q12
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q12.1
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q12.2

Question 13.
Six pumps working together empty a tank in 28 minutes. How long will it take to empty the tank if 4 such pumps are working together?
Solution:
Let the required time be t minutes.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q13
Less pump → More time
Since there is an inverse variation.
x1y1 = x2y2
6 × 28 = 4 × x
x = 42
Hence, the required time = 42 minutes.

Question 14.
Mohit deposited a sum of ₹ 12000 in a Bank at a certain rate of interest for 2 years and earns an interest of ₹ 900. How much interest would be earned for a deposit of ₹ 15000 for the same period and at the same rate of interest?
Solution:
Let the required amount of interest be ₹ x.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q14
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q14.1
Hence, the required amount of interest = ₹ 1125.

Question 15.
A garrison of 120 men has provisions for 30 days. At the end of 5 days, 5 more men joined them. How many days can they sustain on the remaining provision?
Solution:
Let the number of days be x.
Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 Q15
[∵ Remaining days = 30 – 5 = 25]
[Total men = 120 + 5 = 125]
Since there is an inverse variation.
x1y1 = x2y2
120 × 25 = 125 × x
x = 24
Hence, the required number of days be 24.

NCERT Solutions for Class 8 Maths

merupulu.com
RELATED ARTICLES
text books free download
indian constitution
LATEST
telangana history
PRACTICE TEST
CURRENT AFFAIRS

LEAVE A REPLY

Please enter your comment!
Please enter your name here

x
error: Content is protected !!