Frank solutions for Mathematics [English] Class 9 ICSE chapter 7 - Linear Equations [Latest edition]

In the following equations, verify if the given value is a solution of the equation: 5x - 2 = 18; x = 4

In the following equations, verify if the given value is a solution of the equation: 2x - 5 = 3x; x = 3

In the following equations, verify if the given value is a solution of the equation: 3x + 8 = x - 7; x = 3

In the following equations, verify if the given value is a solution of the equation: `2(1)/(2)x + 3(1)/(2)x` = 56 - 2x; x = 7

In the following equations, verify if the given value is a solution of the equation: `(3x - 1)/(4) + (3)/(4)` = 2; x = 2

Solve the following equations for the unknown: 3x + 8 = 35

Solve the following equations for the unknown: 8x - 21 = 3x - 11

Solve the following equations for the unknown: 2x - (3x - 4) = 3x - 4

Solve the following equations for the unknown: `2x + sqrt(2) = 3x - 4 - 3sqrt(2)`

Solve the following equations for the unknown: 15y - 20 = 2y + 6

Solve the following equations for the unknown: 5x + 10 - 4x + 6 = 12x + 20 - 3x + 12

Solve the following equations for the unknown: (a + 2)(2a +5) = 2(a + 1)² + 13

Solve the following equations for the unknown: (6p + 9)² + (8p - 7)² = (10p + 3)² - 71

Solve the following equations for the unknown:

(3x - 1)² + (4x + 1)² = (5x + 1)² + 5

Solve the following equations for the unknown: 3(3x - 4) -2(4x - 5) = 6

Solve the following equation for the unknown: `(4x)/(27) = (8)/(9)`

Solve the following equation for the unknown: `(1.5y)/(3) = (7)/(2)`

Solve the following equation for the unknown: `-(3.4"m")/(2.7) = (10.2)/(9)`

Solve the following equation for the unknown: `(1)/(2)"p" + (3)/(4)"p"` = p - 3

Solve the following equation for the unknown: `(9y)/(4) - (5y)/(3) = (1)/(5)`

Solve the following equation for the unknown: `x/(2) + x/(4) + x/(8)` = 7

Solve the following equation for the unknown: `(2"m")/(3) - "m"/(2)` = 1

Solve the following equation for the unknown: `(2(x - 1))/(9) - (x - 1)/(2)` = 0

Solve the following equation for the unknown: `(4)/(5) x - 21 = (3)/(4)x - 20`

Solve the following equation for the unknown: `("a" - 1)/(2) - ("a" + 1)/(3)` = 5 - a

Solve the following equations for the unknown: `(5)/x - 11 = (2)/x + 16, x ≠ 0`

Solve the following equations for the unknown: `11 - (3)/x = (5)/x + 3`

Solve the following equations for the unknown: `(5)/(3x - 2) - (1)/(8) = 0, x ≠ 0, x ≠ (2)/(3)`

Solve the following equations for the unknown: `(1)/(x - 1) + (4)/(5) = (2)/(3), x ≠ 1`

Solve the following equations for the unknown: `(7)/(x - 2) - (5)/(3)` = 3, x ≠ 2

Solve the following equations for the unknown: `(2x + 3)/(x + 7) = (5)/(8), x ≠ -7`

Solve the following equations for the unknown: `(3x - 5)/(7x - 5) = (1)/(9), x ≠ (5)/(7)`

Solve the following equations for the unknown: `(3)/(x + 1) - (x - 6)/(x^2 - 1) = (12)/(x - 1)`

Solve the following equations for the unknown: `(x + 13)/(x^2 - 1) + (5)/(x + 1) = (7)/(x + 1)`

Solve the following equations for the unknown: `(6x + 7)/(3x + 2) = (4x + 5)/(2x + 3)`

Solve the following equations for the unknown: `2(1)/(5) - (x - 2)/(3) = (x - 1)/(3)`

Solve the following equations for the unknown: `(1)/(2)(y - 1/3) + (1)/(4)(2y + 1/5) = (3)/(4)(y - 1/12)`

Solve the following equations for the unknown: `2 + (3x - 2)/(3x + 2) = (3x + 2)/(x + 1)`

Solve the following equations for the unknown: `(7 x - 1)/(4) - (1)/(3)(2x - (1 - x)/2) = 5(1)/(3)`

Solve the following equations for the unknown: `sqrt(x - 5)` = 3

Solve the following equations for the unknown: `7 - (1)/sqrt(y)` = 0

Solve the following equations for the unknown: `(1)/(5) = (3sqrt(x))/(3)`

Solve the following equations for the unknown: `2sqrt((x - 3)/(x + 5)) = (1)/(3)`

If `(2)/"m" xx 1(1)/(5) = (3)/(7) "of"  2(1)/(2)`, find the value of 'm'.

Solve the following equations: a(x - 2a) +b (x - 2b) = 4ab

Solve the following equations: a(x - b) -b (x - a) = a² - b² 

Solve the following equations: a(x - b) -x (x - 2b) = x + 5(x - b)

Solve the following equations: 8x + a(x - b) = 10(ax - b)

Solve the following equations: a(2x - b) - b(3x - a)+a(x + 1) = b(x + 5)

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

If `"a" = (2x - 3)/(5), "b" = (3x - 2)/(3)`and 2(3a - b) + 1 = 0, find the value of 'x'.

If x = p + 1 and `2.5 + (2"p" + 1)/(3)` = 1.5(2x - 1), find the value of 'p'.

If m = x - 3 and `(4"m" - 3)/(2) - (3"m" - 1)/(5) = (3)/(2)`, find x.

Find the value of a when x = 3 is a solution set of ax² + (a - 4)x + 1 = a.

If a = 2x - 5, 3b = 3x + 1 and if a : b = 3 : 2, find the value of x.

If `(1)/x - (2)/(3"b") + 1` = 0, find the value of b when `(2x + 4)/(8) - (3 - 2x)/(12) = (x - 3)/(6)`

If `x + (6)/"a"` = 11, find the value of a when `4(1)/(3) - (3x - 4)/(5) = (x - 7)/(3)`.

If m(x - 1) = 40, find the value of m when `(x - 1)/(2) = 1 + (x + 1)/(3)`.

Find the value of x for which the expression `x/(5) + 2 "and"  x/(3) - 4` are equal.

Find the value of x if the difference of one-third of (x + 7) and one-fifth of (3x - 2) is 3.

Find the value of x which makes the expressions 10(3x + 12) and 3(9x + 50) equal to each other.

Find the value of x for which the sum of the expression 15(x + 1), 10(x + 2) and 6(x + 3) is 270.

The measures of the angles of a triangle are (3x - 5)°, (3++ 5)° and 6x° Find x and state that the type of triangle formed.

The measures of the angles of a quadrilateral are: (2x - 4)°, (5x - 10)°, (4x - 8)° and (7x - 14)°. find x.

The angles of a triangle are : 2(x + 6)°, 3(x - 1)° and 6(x + 1)°. Find x, and show that the triangle is isosceles.

The side of a square is `(1)/(2)(x + 1)` units, and its diagonals is `(3 - x)/sqrt(2)`

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°. Find the angles.

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

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 measures of angles of a quadrilateral in degrees are x°, (3x-40)°, 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 difference of the squares of two consecutive even natural numbers is 68. Find the two numbers.

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

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?

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.

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 m². 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 m². 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 `33(1)/(2)` 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?

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.

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.

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.

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.

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.

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.

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

Tap A can empty a tank in 6 hours. Tap A along with Tap B together can empty the tank in `3(3)/(7)" hours"`. Find the time Tap B alone will take to empty the tank.

What number increased by 8% of itself gives 1620?

What number increased by 15% of itself gives 2921?

What number decreased by 12% of itself gives 1584?

What number decreased by 18% of itself gives 1599?

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 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.

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 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.

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?

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?

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.

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 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.

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 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.

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?

A 12 liter solution is `33(1)/(3)`% acid. How much water must be added to get the solution having 20% acid?

A 90 kg solution has 10% salt. How much water must be evaporated to have the solution with 20% salt?

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?

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?