Finding solution for consistent pair of LE

Q.

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for nine hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Q.

Six years hence, Rahul's age will be three times his son's age and three years ago, he was nine times as old as his son. Rahul's present age is:

1. 28 years

2. 30 years

3. 32 years

4. 34 years

Q.

Statement 1 : The graph of a linear equation is a straight line.

Statement 2 : The solution of a pair of linear equations is a point common to two lines.

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

Q. One of the solutions of the pair of equations $\frac{a}{x}-\frac{b}{y}=0\text{and}\frac{a{b}^2}{x}+\frac{a^{2}b}{y}=a^2+b^2\text{is:}$

1. $x=a$
2. $y=-b$
3. $x=-a$
4. $x=a{b}^2$

Q. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

1. 8 km/hr, 5 km/hr
2. 8 km/hr, 3 km/hr
3. 5 km/hr, 3 km/hr
4. 9 km/hr, 6 km/hr

Q.

The value of x which satisfies following pair of linear equations is:
(i) x + 2y = -2
(ii) x - 2y = 12

1. (7, 5)

2. (7, -5)

3. (-7, -5)

4. (-7, 5)

Q.

If x + y = 6 and x - y = 2 , then x =___.

1. -4

2. 3

3. 4

4. 2

Q. A man starts his job with a certain salary and earns a fixed increment every year. If his salary was ₹15000 after 4 years of service and ₹18000 after 10 years of service, then find his starting salary and annual increment respectively.

1. Rs. 11000, Rs. 700
2. Rs. 13000, Rs. 700
3. Rs. 11000, Rs. 500
4. Rs. 13000, Rs. 500

Q.

The sum of two numbers is 4 more than the twice of the difference between the two numbers. One of the two numbers is three more than the other number. Find the two numbers.

1. (, )

2. ( , 3)

3. (1, 3)

4. (1, 2)

Q.

54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

1. 34

2. 32

3. 30

4. 24

Q.

Solution for the following pair of linear equations is:
2x + 4y = 8
4x + 8y = 0

1. No Solution

2. All Real Numbers

3. (8, 0)

4. (0, 16)

Q.

The solution of the pair of linear equations
$x+2y=5$ and $7x+3y=13$ is (2, 1).

1. True

2. False

Q. The pair of linear equations $2x+5y=k$ and $kx+15y=18$ has infinitely many solutions if

1. k = 3
2. k = 18
3. k = 6
4. k = 9