Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

$$\displaystyle \frac { 4x }{ 9 } -8=8-\frac { 5x }{ 9 } $$, find $$x$$.

A
$$-16$$

B
$$16$$

C
$$9$$

D
$$\dfrac{3}{16}$$

Solution

Given, $$\displaystyle \frac { 4x }{ 9 } -8=8-\frac { 5x }{ 9 } $$.

Transposing $$x$$ terms to one side, we get,

$$\Longrightarrow\dfrac { 4x }{ 9 } +\dfrac { 5x }{ 9 } =8+8$$

$$\Longrightarrow\displaystyle \frac { 9x }{ 9 } =16$$

$$\Longrightarrow x=16$$.

Hence, option $$B$$ is correct.
Question 2
1 / -0

A man has Rs. $$x$$ with him. He gave $$\dfrac{1}{4}$$th to his wife, $$\dfrac{1}{3}$$rd to his son and Rs. $$1000$$ to his daughter. Find $$x$$.

A
$$2400$$

B
$$2200$$

C
$$2000$$

D
None of the above.

Solution

The total amount of money with the man = Rs. $$x$$.
$$\displaystyle \frac { 1 }{ 4 } x+\frac { 1 }{ 3 } x+1000=x$$

$$\Longrightarrow\displaystyle x-\frac { 1 }{ 4 } x-\frac { 1 }{ 3 } x=1000$$

$$\Longrightarrow\displaystyle \frac { 12x-3x-4x }{ 12 } =1000$$

$$\Longrightarrow\displaystyle 5x=1000\times 12$$

$$x$$ = Rs. $$2400$$
Question 3
1 / -0

The sum of $$5$$, $$9$$ and a number is $$50$$. Find the number.

A
$$35$$

B
$$36$$

C
$$37$$

D
$$38$$

Solution

Let the number be $$ x$$
According to the question,
$$\displaystyle 5+9+x=50$$
$$\therefore \displaystyle x=50-14$$
$$\therefore \displaystyle x=36$$
Question 4
1 / -0

The sum of two numbers is $$30$$. One of the number exceeds the other by $$10$$. Find the number.

A
$$10, -20$$

B
$$-10, 20$$

C
$$10, 20$$

D
$$-10, -20$$

Solution

Let the required number be $$x$$.
Then, the other number will be $$x+10$$
According to the question, sum of the two numbers is $$30$$.
Therefore, $$\displaystyle x+x+10=30$$
$$\therefore \displaystyle 2x=20$$
$$\therefore \displaystyle x=10$$
The numbers are $$10$$ and $$10+10=20$$.
Question 5
1 / -0

The four consecutive numbers add up to $$74$$. What are these integers?

A
$$18, 19, 20, 21$$

B
$$17, 18, 19, 20$$

C
$$20, 18, 18, 19$$

D
$$16, 17, 18, 19$$

Solution

Let the first integer$$ = p$$
$$\displaystyle \therefore $$ the second integer $$= p+1$$
and the third consecutive integer $$= p+2$$ and fourth $$= p+3$$
$$\displaystyle \because $$ Sum of four consecutive numbers = $$74$$
$$\displaystyle p+(p+1)+(p+2)+(p+3)=74$$
$$\Longrightarrow \displaystyle 4p+6=74$$
$$\Longrightarrow 4p=68$$

$$\Longrightarrow \displaystyle p=\frac { 68 }{ 4 } $$
$$\therefore p=17$$
1 st integer $$= 17$$
2nd integer $$= 18$$
3rd integer $$= 19$$
4 th integer $$= 20$$

So, option B is correct.
Question 6
1 / -0

Solve $$8(3+2x)=13x$$ and find the value of $$ x$$

A
$$-8$$

B
$$8$$

C
$$\dfrac{1}{8}$$

D
$$\dfrac{-1}{8}$$

Solution

Given, $$ \displaystyle 8(3+2x)=13x$$

$$\Rightarrow 24+16x=13x$$ ...[By Distribution Law]

Transposing $$x$$ terms to one side, we get,

$$\Rightarrow\displaystyle 16x-13x = -24$$

$$\Rightarrow\displaystyle 3x=-24$$

$$\Rightarrow x=\dfrac{-24}{3}$$

$$\Rightarrow x=-8$$
Question 7
1 / -0

The sum of three consecutive even integers is $$72$$. Find the smallest number

A
$$24$$

B
$$22$$

C
$$26$$

D
None

Solution

Let the three consecutive numbers be $$ x, x+2$$ and $$x+4$$.
Sum = $$\displaystyle x+x+2+x+4$$
$$\therefore 3x + 6 = 72$$
$$\Longrightarrow 3x=66$$
$$\Longrightarrow x=22$$
Question 8
1 / -0

The sum of $$6$$ consecutive numbers is $$105$$. Find the smallest number.

A
$$13$$

B
$$15$$

C
$$14$$

D
$$12$$

Solution

Let the 6 consecutive numbers be $$x, x+1, x+2, x+3, x+4$$ and $$x+5$$
$$\Longrightarrow \displaystyle x+x+1+x+2+x+3+x+4+x+5=105$$
$$\Longrightarrow \displaystyle 6x+15=105$$
$$\therefore 6x=90$$
$$\therefore x=15$$
Question 9
1 / -0

The sum of three consecutive multiples of $$5$$ is $$45$$. Which is the smallest of the three multiples?

A
$$10$$

B
$$5$$

C
$$15$$

D
$$20$$

Solution

Let $$5x$$ be the smallest multiple of $$5$$.
Then, the three consecutive multiples shall be $$5x$$, $$5x+5$$ and $$5x+10$$
According to the question,
$$\displaystyle 5x+5x+5+5x+10=45$$
$$\therefore \displaystyle 5x+5x+5x=45-15$$
$$\therefore \displaystyle 15x=30$$
$$\therefore \displaystyle x=2$$
$$\displaystyle \therefore $$ Smallest multiple $$= 5x = 5\times 2 = 10$$
Question 10
1 / -0

The length of a rectangle is $$ 1\frac { 3 }{ 4 } $$ of its breadth. If perimeter is $$66$$. find the length of rectangle.

A
$$12$$

B
$$21$$

C
$$20$$

D
$$11$$

Solution

Let breadth of rectangle be $$x$$
Length = $$\displaystyle 1\frac { 3 }{ 4 } \times x=\frac { 7 }{ 4 } x$$ ....given

According to the question,
$$\displaystyle 2\left( \frac { 7 }{ 4 } x+x \right) =66$$

$$\Longrightarrow 2\left( \dfrac { 7x+4x }{ 4 } \right) =66$$

$$\Longrightarrow\displaystyle 11x=66\times 2$$

$$\Longrightarrow\displaystyle x=12$$

Length =$$\dfrac { 7 }{ 4 } \times 12=21$$

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 36

Result

Linear Equations in One Variable Test - 36

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SHARING IS CARING

Question 1

$$-16$$

$$16$$

$$9$$

$$\dfrac{3}{16}$$

Solution

Question 2

$$2400$$

$$2200$$

$$2000$$

None of the above.

Solution

Question 3

$$35$$

$$36$$

$$37$$

$$38$$

Solution

Question 4

$$10, -20$$

$$-10, 20$$

$$10, 20$$

$$-10, -20$$

Solution

Question 5

$$18, 19, 20, 21$$

$$17, 18, 19, 20$$

$$20, 18, 18, 19$$

$$16, 17, 18, 19$$

Solution

Question 6

$$-8$$

$$8$$

$$\dfrac{1}{8}$$

$$\dfrac{-1}{8}$$

Solution

Question 7

$$24$$

$$22$$

$$26$$

None

Solution

Question 8

$$13$$

$$15$$

$$14$$

$$12$$

Solution

Question 9

$$10$$

$$5$$

$$15$$

$$20$$

Solution

Question 10

$$12$$

$$21$$

$$20$$

$$11$$

Solution

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