Simple Linear Equations — Multiple Choice Questions

For $20x$ ÷ 3 = 40; the value of $x$ is:

1. 6

2. -6

3. $\dfrac{2}{3}$

4. $\dfrac{3}{2}$

Answer

Solving,

$\Rightarrow 20x \div 3 = 40 \\[1em] \Rightarrow \dfrac{20x}{3} = 40 \\[1em] \Rightarrow x = \dfrac{40 \times 3}{20} \\[1em] \Rightarrow x = 2 \times 3 = 6.$

Hence, option 1 is the correct option.

For $\dfrac{2x}{3}$ - 5 = 3; the value of $x$ is:

1. -12

2. 12

3. 3

4. -3

Answer

Solving,

$\Rightarrow \dfrac{2x}{3} - 5 = 3 \\[1em] \Rightarrow \dfrac{2x}{3} = 8 \\[1em] \Rightarrow 2x = 24 \\[1em] \Rightarrow x = 12.$

Hence, option 2 is the correct option.

For 2 - 3(5 - $x$) = 8; the value of $x$ is:

1. 13

2. -13

3. 7

4. -7

Answer

Solving,

$\Rightarrow 2 - 3(5 - x) = 8 \\[1em] \Rightarrow 2 - 15 + 3x = 8 \\[1em] \Rightarrow 3x - 13 = 8 \\[1em] \Rightarrow 3x = 21 \\[1em] \Rightarrow x = 7.$

Hence, option 3 is the correct option.

For 5 + $\dfrac{x-1}{2} = x$; the value of $x$ is:

1. -3

2. 3

3. -9

4. 9

Answer

Solving,

$\Rightarrow 5 + \dfrac{x - 1}{2} = x \\[1em] \Rightarrow 10 + x - 1 = 2x \\[1em] \Rightarrow 9 + x = 2x \\[1em] \Rightarrow x = 9.$

Hence, option 4 is the correct option.

Subtracting 6 from three times a number gives 9, the number is:

1. 5

2. -5

3. 6

4. -6

Answer

Let the number be $x$.

Solving,

$\Rightarrow 3x - 6 = 9 \\[1em] \Rightarrow 3x = 15 \\[1em] \Rightarrow x = 5.$

∴ The number is 5.

Hence, option 1 is the correct option.

In a cricket match, Rohit scored twice as many runs as Piyush. Together, their runs fell four short of a century. The runs scored by Piyush are:

1. 64

2. 32

3. 26

4. 52

Answer

Let the runs scored by Piyush be $x$, then the runs scored by Rohit = $2x$.

Their runs together = 100 − 4 = 96

Solving,

$\Rightarrow x + 2x = 96 \\[1em] \Rightarrow 3x = 96 \\[1em] \Rightarrow x = 32.$

∴ The runs scored by Piyush are 32.

Hence, option 2 is the correct option.

When expressions $x$ - 5 and 5 - $x$ are equal, the value of $x$ is:

1. 0

2. 5

3. 10

4. none of these

Answer

Solving,

$\Rightarrow x - 5 = 5 - x \\[1em] \Rightarrow x + x = 5 + 5 \\[1em] \Rightarrow 2x = 10 \\[1em] \Rightarrow x = 5.$

Hence, option 2 is the correct option.

For equation $\dfrac{x}{3} + 2x$ = 14, the value of $x$ is:

1. 14

2. 42

3. 18

4. 6

Answer

Solving,

$\Rightarrow \dfrac{x}{3} + 2x = 14 \\[1em] \Rightarrow \dfrac{x + 6x}{3} = 14 \\[1em] \Rightarrow \dfrac{7x}{3} = 14 \\[1em] \Rightarrow 7x = 42 \\[1em] \Rightarrow x = 6.$

Hence, option 4 is the correct option.

A number is multiplied by 5 and then 8 is subtracted from the product. If result so obtained is 12; the number is:

1. 4

2. $\dfrac{4}{5}$

3. $\dfrac{5}{4}$

4. -4

Answer

Let the number be $x$.

Solving,

$\Rightarrow 5x - 8 = 12 \\[1em] \Rightarrow 5x = 20 \\[1em] \Rightarrow x = 4.$

∴ The number is 4.

Hence, option 1 is the correct option.

Ruhi is 7 years older than her brother. If the sum of their ages is 33 years; the age of Ruhi (in years) is:

1. 27

2. 25

3. 20

4. 13

Answer

Let the age of Ruhi's brother be $x$ years, then Ruhi's age = ($x$ + 7) years.

Solving,

$\Rightarrow x + (x + 7) = 33 \\[1em] \Rightarrow 2x + 7 = 33 \\[1em] \Rightarrow 2x = 26 \\[1em] \Rightarrow x = 13.$

∴ Age of Ruhi = $x$ + 7 = 13 + 7 = 20 years

Hence, option 3 is the correct option.

A's age is 5 years more than three times the age of B. If sum of their ages is 57 years, the age of B is:

1. 26 years

2. 22 years

3. 13 years

4. none of these

Answer

Let the age of B be $x$ years, then A's age = ($3x$ + 5) years.

Solving,

$\Rightarrow x + (3x + 5) = 57 \\[1em] \Rightarrow 4x + 5 = 57 \\[1em] \Rightarrow 4x = 52 \\[1em] \Rightarrow x = 13.$

∴ The age of B is 13 years.

Hence, option 3 is the correct option.

In an examination the highest score of marks is 7 more than twice the lowest score. If the highest score is 87, the lowest score is:

1. 40

2. 47

3. 73

4. 20

Answer

Let the lowest score be $x$.

Solving,

$\Rightarrow 2x + 7 = 87 \\[1em] \Rightarrow 2x = 80 \\[1em] \Rightarrow x = 40.$

∴ The lowest score is 40.

Hence, option 1 is the correct option.

One-fourth of a number is 3 more than 7. The number is:

1. 10

2. 20

3. 40

4. 16

Answer

Let the number be $x$.

Solving,

$\Rightarrow \dfrac{x}{4} = 3 + 7 \\[1em] \Rightarrow \dfrac{x}{4} = 10 \\[1em] \Rightarrow x = 40.$

∴ The number is 40.

Hence, option 3 is the correct option.

Adding 3 to three-fourths of a number is 21. The number is:

1. 24

2. 32

3. 48

4. 16

Answer

Let the number be $x$.

Solving,

$\Rightarrow \dfrac{3}{4}x + 3 = 21 \\[1em] \Rightarrow \dfrac{3}{4}x = 18 \\[1em] \Rightarrow 3x = 72 \\[1em] \Rightarrow x = 24.$

∴ The number is 24.

Hence, option 1 is the correct option.

For $3(x - 1) = x - 11$; the value of $x$ is:

1. 4

2. -4

3. -5

4. 5

Answer

Solving,

$\Rightarrow 3(x - 1) = x - 11 \\[1em] \Rightarrow 3x - 3 = x - 11 \\[1em] \Rightarrow 3x - x = -11 + 3 \\[1em] \Rightarrow 2x = -8 \\[1em] \Rightarrow x = -4.$

Hence, option 2 is the correct option.