# 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.

## Chapter 7 - Linear Equations Excercise Ex. 7.1

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equation for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

Solve the following equations for the unknown:

If 7(3 - 4x) = 1, evaluate 2x^{2} + 7x + 6

## Chapter 7 - Linear Equations Excercise Ex. 7.2

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.

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

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

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

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

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

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

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

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

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

Find two consecutive even numbers, whose sum is 38.

Two complementary angles differ by 14^{o}. Find the angles.

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

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

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

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

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

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.

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.

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.

## Chapter 7 - Linear Equations Excercise Ex. 7.3

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.

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.

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.

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.

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.

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.

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.

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?

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.

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.

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.

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.

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?

## Chapter 7 - Linear Equations Excercise Ex. 7.4

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.

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 m^{2}. Find the length and the breadth of
the field.

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.

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 m^{2}. Find the dimensions of the field.

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.

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?

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.

What number increased by 15% of itself gives 2921?

What number decreased by 12% of itself gives 1584?

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

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.

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.

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?

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?

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.

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?

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?

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

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?

## Chapter 7 - Linear Equations Excercise Ex. 7.5

^{2}.Find the length and breadth of the field.

^{2}. Find the length and breadth of the field.

^{2}. Find the dimensions of the field.

^{2}. Find the length and breadth of the room.

## Chapter 7 - Linear Equations Excercise Ex. 7.6

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