Equations with Two Variables

Q. 8 men and 12 boys can finish a piece of work in 5 days, while 6 men and 8 boys can finish it in 7 days. Find time taken by a man and a boy alone to finish the same work.

1. 80, 150
2. 50, 120
3. 60, 130
4. 70, 140

Q.

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?

1. 2 m, 20 m

2. 26 m, 20 m

3. 56 m, 40 m

4. 2 m, 3 m

Q.

1. x-2y=0

2. x+2y=0

3. x+y=0

4. 2x-y=0

Q. Express this statement as an equation:
My age is 3 years less than twice the age of my brother. Assume that my brother’s age is x and my age is y.

1. 2x - y = 3
2. x - 2y = 3
3. 2x + y = 3
4. 3x - 2y = 0

Q.

Which of the following are linear equations in 2 variables?

1. 5x=3y-6

2. 5x+3y+6z=18

3. 5x+3y-18=0

4. x+8=20

Q.

A plane left 30 minutes later than its scheduled time. In order to reach the destination which is 1500 km away on time, it has to increase its speed by 250 km/hr. Find its original speed.

1. 1000 km/hr

2. 750 km/hr

3. 800 km/hr

4. 680 km/hr

Q.

Which of the following are Pair of Linear Equation in two variables?

1. x + 2 = 0; a + 2b = 0

2. x + y - 3 = 0; 4a + 2b + c = 24

3. 2x + y = 2; 3x - z=2

4. 12x + 4y + 3 = 0; 4x + 4y + 4 = 0

Q.

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km then total time taken increases by 11 hours. Find the speed of the stream and speed of the boat.

1. 4, 7

2. 7, 8

3. 3, 2

4. 6, 3

Q.

Based on the graph, the pair of linear equations has _______________solution(s).

1. Only one

2. Infinite

3. Four

4. Zero

Q.

1. x+y=0

2. x+2y=0