Chapter 7 : Linear Equations - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 7 - Linear Equations Excercise Ex. 7.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solve the following equation for the unknown:

  

Solution 3

Question 4

Solve the following equation for the unknown:

  

Solution 4

Question 5

Solve the following equation for the unknown:

  

Solution 5

Question 6

Solve the following equation for the unknown:

  

Solution 6

Question 7

Solve the following equation for the unknown:

  

Solution 7

Question 8

Solve the following equation for the unknown:

  

Solution 8

Question 9

Solve the following equation for the unknown:

  

Solution 9

Question 10

Solve the following equation for the unknown:

  

Solution 10

Question 11

Solve the following equation for the unknown:

  

Solution 11

Question 12

Solve the following equation for the unknown:

  

Solution 12

Question 13

Solve the following equations for the unknown:

  

Solution 13

Question 14

Solve the following equations for the unknown:

  

Solution 14

Question 15

Solve the following equations for the unknown:

  

Solution 15

Question 16

Solve the following equations for the unknown:

Solution 16

Question 17

Solve the following equations for the unknown:

  

Solution 17

Question 18

Solve the following equations for the unknown:

  

Solution 18

Question 19

Solve the following equations for the unknown:

  

Solution 19

Question 20

Solve the following equations for the unknown:

Solution 20

Question 21

Solve the following equations for the unknown:

Solution 21

Question 22

Solve the following equations for the unknown:

Solution 22

Question 23

Solve the following equations for the unknown:

  

Solution 23

Question 24

Solve the following equations for the unknown:

  

Solution 24

Question 25

Solve the following equations for the unknown:

Solution 25

Question 26

Solve the following equations for the unknown:

  

Solution 26

Question 27

Solve the following equations for the unknown:

  

Solution 27

Question 28

Solve the following equations for the unknown:

  

Solution 28

Question 29

Solve the following equations for the unknown:

  

Solution 29

Question 30

Solve the following equations for the unknown:

  

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

If 7(3 - 4x) = 1, evaluate 2x2 + 7x + 6

Solution 33

Question 34

  

Solution 34

Question 35

  

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

  

Solution 41

Chapter 7 - Linear Equations Excercise Ex. 7.2

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8

Solution 8

Question 9

The measures of angles of a triangle are (9x - 5)°, (7x + 5)° and 20x°. Find the value of x. Also, show that the triangle is isosceles.

Solution 9

Question 10

The difference of the squares of two consecutive even natural numbers is 68. Find the two numbers.

Solution 10

Question 11

For two consecutive odd natural numbers, the square of bigger number exceeds the square of smaller number by 72. Find the two numbers.

Solution 11

Question 12

The sum of three consecutive natural numbers is 216. Find the numbers.

Solution 12

Question 13

The sum of three consecutive odd natural numbers is 99. Find the numbers.

Solution 13

Question 14

Find the number which, when added to its half, gives 60.

Solution 14

Question 15

Twice a number decreased by 15, equals 25. Find the number.

Solution 15

Question 16

The sum of two numbers is 50, and their difference is 10. Find the numbers.

Solution 16

Question 17

A number is as much greater than 21 as it is less than 71. Find the number.

Solution 17

Question 18

Divide 300 into two parts so that half of the one part is less than the other by 48.

Solution 18

Question 19

Find two consecutive even numbers, whose sum is 38.

Solution 19

Question 20

Two complementary angles differ by 14o. Find the angles.

Solution 20

Question 21

Two angles are supplementary and their measures are (7x+6)o and (2x-15)o. Find the measures of the angles.

Solution 21

Question 22

The measures of angles of a quadrilateral in degrees are xo, (3x-40)o, 2xo and (4x+20)o. Find the measures of the angles.

Solution 22

Question 23

Two numbers are in the ratio 2:3. If their sum is 150, find the numbers

Solution 23

Question 24

Two numbers are in the ratio 11:13. If the smaller number is 286, find the bigger one.

Solution 24

Question 25

The sum of the squares of two consecutive odd natural numbers is 650. Find the two numbers.

Solution 25

Question 26

The denominator of a fraction is 18 more than the numerator. If 1 is added to both the numerator and denominator, the value of the fraction equals the value of fraction obtained by adding 8 to the numerator and 15 to the denominator. Find the fraction.

Solution 26

Question 27

In a two-digit number, the digit at the ten's place is 4 times the digit at the unit's place.The sum of the digits and the number is 92. Find the two digit number.

Solution 27

Question 28

In a two digit number, the ratio of the digits at the unit's place and the ten's place is 3:2. If the digits are reversed, the resulting number is 27 more than the original number. Find the two digit number.

Solution 28

Chapter 7 - Linear Equations Excercise Ex. 7.3

Question 1

Shweta's age is six times that of Jayeeta's age. 15 years hence Shweta will be three times as old as Jayeeta; find their ages.

Solution 1

Question 2

The ages of P and Q are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their ages.

Solution 2

Question 3

The present age of a man is double the age of his son. After 8 years, the ratio of their ages will be 7 : 4. Find the present ages of the man and his son.

Solution 3

Question 4

A man covers a distance of 95 km in 5 hours; partly on foot at the rate of 5 km/h and partly on a motorcycle at 40km/h. Find the distance travelled by him on the motorcycle.

Solution 4

Question 5

The distance between two places Bangalore and Hyderabad is 660 km. Anand starts from Bangalore with a certain uniform speed while Sonu starts from Hyderabad at the same time with a uniform speed that is 4km more than that of Anand. If they meet each other after 5 hours, find the speed of each.

Solution 5

Question 6

A man went to market at a speed of 4 km/h and returned at a speed of 3km/h. If he took 30 minutes more in returning, find the distance of the market from his home.

Solution 6

Question 7

A takes 4hours more than B in walking 30 km. If A doubles his speed, he will take 1hr less than B. Find the speeds of A and B.

Solution 7

Question 8

If a motorcyclist drives at the rate of 24km/h, he reaches his destination 5 minutes too late. If he drives at the rate of 30 km/h, he reaches his destination 4minutes too soon. How far is his destination?

Solution 8

Question 9

If a boy walks to his school at a speed of 4km/h, he reaches the school 10 minutes before time. If he walks at 3km/h, he reaches the school 10 minutes late. Find the distance between his house and school.

Solution 9

Question 10

Two planes start from a city and fly in opposite directions, one averaging a speed of 40 km/h more than that of the other. If they are 3400km apart after 5 hours, find their average speeds.

Solution 10

Question 11

A steamer goes in downstream from one port to another in 4hours. It covers the same distance in upstream in 5 hours. If the speed of the stream be 2 km/h, find the distance between the two ports.

Solution 11

Question 12

The speed of a boat in still water is 8km/h. It takes the same time in going 20km in downstream as it takes in going 12 km upstream. Find the speed of the stream.

Solution 12

Question 13

A police car is ordered to chase a speeding car which is 5 km ahead and is travelling at an average speed of 80 km/h. The police car is running at an average speed of 100 km/h. How long it take for the police car to overtake the speeding car?

Solution 13

Chapter 7 - Linear Equations Excercise Ex. 7.4

Question 1

The length of a rectangle is 30 cm more than its breadth. The perimeter of the rectangle is 180 cm. Find the length and the breadth of the rectangle.

Solution 1

Question 2

The perimeter of a rectangular field is 80 m. If the breadth is increased by 2 m and the length is decreased by 2 m, the area of the field increases by 36 m2. Find the length and the breadth of the field.

Solution 2

Question 3

In an isosceles triangle, each of the two equal sides is 4 cm more than the base. If the perimeter of the triangle is 29 cm, find the sides of the triangle.

Solution 3

Question 4

The perimeter of a rectangular field is 100 m. If its length is decreased by 2 m and breadth increased by 3 m, the area of the field is increased by 44 m2. Find the dimensions of the field.

Solution 4

Question 5

A and B together can complete a piece of work in 6 days. A can do it alone in 10 days. Find the number of days in which B alone can do the work.

Solution 5

Question 6

A and B together can do a piece of work in 4 days, but A alone can do it in 12 days. How many days would B alone take to do the same piece of work?

Solution 6

Question 7

A tap can fill a tank in 12 hours while another tap can fill the same tank in x hours. Both the taps if opened together can fill the tank in 6 hours and 40 minutes. Find the time the second tap will take to fill the tank.

Solution 7

Question 8

What number increased by 15% of itself gives 2921?

Solution 8

Question 9

What number decreased by 12% of itself gives 1584?

Solution 9

Question 10

The sum of two numbers is 99. If one number is 20% more than the others, find the two numbers.

Solution 10

Question 11

In a factory a worker is paid Rs. 20 per hour for normal work and double the rate for overtime work. If he worked for 56 hours in a week, find the number of hours of his normal work if he receives Rs. 1440 in all.

Solution 11

Question 12

A boy played 100 games, gaining Rs. 50 on each game that he won, and losing Rs. 20 for each game that he lost. If on the whole he gained Rs. 800, find the number of games that he won.

Solution 12

Question 13

In a shooting competition a marksman receives Rs. 50 if he hits the mark and pays Rs. 20 if he misses it. He tried Rs. 100 shots and was paid Rs. 100. How many times did he hit the mark?

Solution 13

Question 14

There are certain benches in a classroom. If 4 students sit on each bench, 3 benches are left vacant; and if 3 students sit on each bench, 3 students are left standing. What is the total number of students in the class?

Solution 14

  

Question 15

A man sells an article and makes a profit of 6%. Had he bought the article at a price 4% less and sold at a price higher by Rs. 7.60, he would have made a profit of 12%. Find his cost price.

Solution 15

Question 16

A man invested Rs. 35000, a part of it at 12% and the rest at 14%. If he received a total annual interest of Rs. 4460, how much did he invest at each rate?

Solution 16

Question 17

A 700 g dry fruit pack costs Rs. 72. It contains some cashew kernels and the rest as dry grapes. If cashew kernel costs Rs. 96 per kg and dry grapes cost Rs. 112 per kg, what were the quantities of the two dry fruits separately?

Solution 17

Question 18

A 12 litre solution is  acid. How much water must be added to get the solution having 20% acid?

Solution 18

Question 19

A man leaves half his property to his wife, one-third to his son, and the remaining to his daughter. If the daughter's share is Rs. 15000, how much money did the man leave? How much money did his wife get?

Solution 19

Chapter 7 - Linear Equations Excercise Ex. 7.5

Question 1
A's age is six times that of B's age. 15 years hence A will be three times as old as B; find their ages.
Solution 1
Question 2
The ages of A and B are in the ratio 7:5.Ten years hence, the ratio of their ages will be 9:7. Find their ages.
Solution 2
Question 3
The present age of a man is double the age of his son. After 8 years, the ratio of their ages will be 7:4. Find the present ages of the man and his son.
Solution 3
Question 4
The age of a man is three times the age of his son. After 10 years, the age of the man will be double that of his son. Find their present ages.
Solution 4
Question 5
The difference between the ages of two brothers is 10 years, and 15 years ago their ages were in the ratio 2:1. Find the ratio of their ages 15 years hence.
Solution 5
Question 6
A boy is now one-third as old as his father. Twelve years hence he will be half as old as his father. Determine the present ages of the boy and that of his father.
Solution 6
Question 7
5 years ago, the age of a man was 7 times the age of his son. The age of the man will be 3 times the age of his son in 5 years from now. How old are the man and his son now?
Solution 7
Question 8
A man is double his son's age. Twenty years ago, he was six times his son's age. Find the present age of the father and the son.
Solution 8
Question 9
The length of a rectangle is 30 more than its breadth. The perimeter of the rectangle is 180 cm. Find the length and breadth of the rectangle.
Solution 9
Question 10
The perimeter of a rectangular field is 80m. If the breadth is increased by 2 m and the length is decreased by 2 m, the area of the field increases by 36m2.Find the length and breadth of the field.
Solution 10
Question 11
The length of a rectangle is 3 cm more than its breadth. If the perimeter of the rectangle is 18cm, find the length and breadth of the rectangle.
Solution 11
Question 12
The perimeter of a rectangular field is 140 m. If the length of the field is increased by 2 m and the breadth decreased by 3m, the area is decreased by 66 m2. Find the length and breadth of the field.
Solution 12
Question 13
In an isosceles triangle, each of the two equal sides is 4 cm more than its base. If the perimeter of the triangle is 29cm, find the sides of the triangle.
Solution 13
Question 14
The breadth of a rectangular room is 2 m less than its length. If the perimeter of the room is 14m, find it's dimensions.
Solution 14

Question 15
The perimeter of a rectangular field is 100m.If its length is decreased by 2m and breadth increased by 3 m, the area of the field is increased by 44m2. Find the dimensions of the field.
Solution 15
Question 16
The length of a room exceeds its breadth by 3 m. If both the length and breadth, are increased by 1m, then the area of the room is increased by 18 cm2. Find the length and breadth of the room.
Solution 16
Question 17
A and B together can complete a piece of work in 6 days. A can do it alone in 10 days. Find the number of days in which B alone can do the work.
Solution 17
Question 18
A and B together can complete a piece of work in 4 days, but A alone can do it a in 12 days. How many days would B alone take to do the same work.
Solution 18
Question 19
A tap can fill a tank in 12 hrs while another tap can fill the same tank in x hours. Both the taps if opened together fill the tank in 6 hrs and 40 minutes. Find the time the second tap will take to fill the tank.
Solution 19
Question 20

Solution 20

Chapter 7 - Linear Equations Excercise Ex. 7.6

Question 1
What number increased by 8% of itself gives 1620?
Solution 1
Question 2
What number increased by 15% of itself gives 2921?
Solution 2
Question 3
What number decreased by 12% of itself gives 1584?
Solution 3
Question 4
What number decreased by 18% of itself gives 1599?
Solution 4
Question 5
In a factory a worker is paid Rs 20 per hour for normal work and double the rate for overtime work. If he worked for 56 hours in a week, find the number of hours of his normal work if he receives Rs 1440 in all.
Solution 5
Question 6
A worker is employed on the condition that he will be paid Rs 60 for each day that he works and fined Rs 20 for each day that he remains absent. If he is paid Rs 1000 for the month of September, find the number of days that he worked.
Solution 6
Question 7
A boy played 100 games, gaining Rs 50 on each game that he won, and losing Rs 20 for each game that he lost. If on the whole he gained Rs 800, find the number of games that he won.
Solution 7
Question 8
In a factory male workers are paid one and a half times more than their female counterparts for each hour of work. In a particular week a husband and wife team worked for a total of 60 hours with the husband working twice as much as his wife. The total amount earned by both is Rs 960. If the husband's earning is 4 times that of his wife, find the number of hours each worked.
Solution 8
Question 9
In a shooting competition a marks man receives 50 paise if he hits the mark and pays 20 paise if he misses it. He tried 100 shots and was paid Rs 29. How many times did he hit the mark?
Solution 9
Question 10
There are certain benches in a classroom. If 4 students sit on each bench, three benches are left vacant and if 3 students sit on each bench, 3 students are left standing. What is the total number of students in the class?
Solution 10
Question 11
In a class there are a certain number of seats. If each student occupies one seat, 9 students remain standing and if 2 students occupy one seat, 7 seats are left empty. Find the number of seats in the class.
Solution 11
Question 12
A man sells an article and makes a profit of 6%.Had he bought the article at a price 4% less and sold at a price higher by Rs 7.60, he would have made a profit of 12%. Find his cost price.
Solution 12
Question 13
A man buys two articles at Rs 410. He sells both at the same price. On one he makes a profit of 15% and on the other a loss of 10%. Find the cost price of both.
Solution 13
Question 14
A man invested Rs 35000, a part of it at 12% and the rest at 14%. If he received a total annual interest of Rs 4460, how much did he invest at each rate?
Solution 14
Question 15
A 700g dry fruit pack costs Rs 72. It contains some cashew kernels and the rest as dry grapes. If cashew kernels cost Rs 96 per kg and dry grapes costs Rs 112 per kg, what were the quantities of the two dry fruits separately.
Solution 15
Question 16
In an election there were two candidates. A total of 9791 votes were polled. 116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had. By what margin did the successful candidate win?
Solution 16
Question 17
Solution 17
Question 18
A 90 kg solution has 10% salt. How much water must be evaporated to have the solution with 20% salt?
Solution 18
Question 19
How many kilograms of tea at Rs 50 per kg should be mixed with 35 kg of tea costing Rs 60 per kg so as to sell the mixture at Rs 57 per kg without gaining or losing anything in transaction?
Solution 19
Question 20
A man leaves half his property to his wife, one-third to his son and the remaining to his daughter. If the daughter's share is Rs 15000, how much money did the man leave? How much money did his wife get?
Solution 20

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