Linear Equations in One Variable Test

Result

Linear Equations in One Variable Test - 17

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

On a three day hiking trip you hiked the same distance (in km) on both first and second days.You hiked $$5$$ km on the third day. If you hiked a total of $$19$$ km, how many kilometer were left to hike after the first day?

A
$$11$$ km

B
$$12$$ km

C
$$9$$ km

D
$$10$$ km

Solution

Let the distance hiked on first two days be $$x$$ km each.
Then, $$x+x+5=19$$
$$\Rightarrow 2x+5=19$$
$$\Rightarrow \displaystyle 2x=19-5=14$$
$$\Rightarrow x=\dfrac{14}{2}=7$$
$$\therefore $$ distance left to be hiked after the first day
$$=(7+5)=12$$ km.
Question 2
1 / -0

Find two consecutive even whole numbers, whose sum is $$38$$.

A
$$10$$ and $$14$$

B
$$18$$ and $$20$$

C
$$16$$ and $$34$$

D
$$12$$ and $$29$$

Solution

Let the two consecutive numbers be $$x$$ and $$x+2$$.

Given their sum is $$38$$.

Therefore, $$x+x+2 = 38$$

$$\Rightarrow 2x = 36$$

$$\Rightarrow x = 18$$

Other number is $$x+2=18+2=20$$.

So, the numbers are $$18$$ and $$20$$.
Question 3
1 / -0

Solve:
$$\displaystyle \frac{7x\, -\, 1}{4}\, - \, \frac{1}{3}(2x\, -\, \frac{1\, -\,x}{2})\,

=\, {6}\frac{1}{3}$$.

A
7

B
5

C
-7

D
3

Solution

$$\displaystyle \frac{7x\, -\, 1}{4}\, - \, \frac{1}{3}(2x\, -\, \frac{1\, -\,x}{2})\, =\, {6}\frac{1}{3}$$
$$=>\dfrac{7x-1}{4}-\dfrac{2x}{3}+\dfrac{1-x}{6}-\dfrac{19}{3}=0$$
$$=>\dfrac{21x-3-8x+2-2x-76}{12}=0$$
$$=>11x-77=0$$
$$=>x=\dfrac{77}{11}$$
$$=>x=7$$
Question 4
1 / -0

You are decorating a gift pack with $$15$$ flowers. You want an equal number of flowers in each of the $$3$$ rows on the gift pack. Which equation would you use to find the number of flowers, $$r$$ in each row?

A
$$r+3=15$$

B
$$15-r=3$$

C
$$3r=15$$

D
$$\displaystyle \frac{3}{r}=15$$

Solution

We have, number of rows $$\times $$ Number of flowers in each row$$=$$ Total number of flowers.
$$\Rightarrow 3\times r=15$$
$$\Rightarrow 3r=15$$
Hence, option C is correct.
Question 5
1 / -0

If a number with $$12$$ has the same ratio as $$8$$ having with $$10$$, then the number is :

A
$$15$$

B
$$9.6$$

C
$$7.5$$

D
$$10$$

Solution

Let the required number be $$x$$.
$$\therefore$$$$\displaystyle{\frac{x}{12} = \frac{8}{10} \Rightarrow x = 9.6}$$
Hence, option 'B' is correct.
Question 6
1 / -0

Which of the following equation is not a linear equation?

A
$$2x + 3 = 7x - 2$$

B
$$\displaystyle \frac{2}{3}x + 5 = 3x - 4$$

C
$$\displaystyle x^2 + 3 = 5x - 3$$

D
$$\displaystyle (x - 2)^2 = x^2 + 8$$

Solution

An algebraic equation is said to be linear if the variable or variables in the equation are of the first degree.

In option $$A$$, all the $$x$$ terms have a degree $$1$$. So, it is a linear equation.

In option $$B$$, all the $$x$$ terms have a degree $$1$$. So, it is a linear equation.

In option $$C$$, $$ x^{2}+3=5x-3, x $$ is raised to the power $$2$$.
So, $$x^{2}+3=5x-3$$ is not a linear equation.

In option $$D$$, $$(x-2)^2=x^2+8 $$
$$\Rightarrow x^2-4x+4=x^2+8$$
$$\Rightarrow -4x=4$$
i.e, the $$x$$ term has a degree $$1$$. So, it is a linear equation.

Hence, Option $$C$$ is the correct option.
Question 7
1 / -0

The three even consecutive integers whose sum is 90 are

A
$$26 , 30, 34$$

B
$$24, 32, 34$$

C
$$24, 28, 38$$

D
$$28, 30, 32$$

Solution

Let, the three even consecutive integers be $$x, x+2, x+4$$
A.T.Q,
$$x+x+2+x+4=90$$
$$\implies 3x+6=90$$
$$\implies 3x=90-6=84$$
$$\implies x=\dfrac{84}{3}=28$$
$$\therefore$$ The three even consecutive integers are $$ 28,30, 32$$
Question 8
1 / -0

A is 2 years older than B who is twice as old as C If the total of the ages of A, B and C be 27 years then how old is B?

A
7 years

B
8 years

C
9 years

D
10 years

Solution

Let C' age $$= x$$ years Then
B's age $$= 2x$$ years
As age $$(2 x + 2)$$ years
Given $$(2x + 2 )$$ years
$$\displaystyle \Rightarrow 5x+2=27\Rightarrow 5x=25\Rightarrow x=5$$
$$\displaystyle \therefore $$ B's age $$= (2 \times 5)$$ years $$=10$$ years.
Question 9
1 / -0

The sum of the ages of 5 children born at intervals of 3 years each is 50 years What is the age of the youngest child?

A
4 years

B
8 years

C
10 years

D
6 years

Solution

Let the age of the youngest child be $$x$$ years
Then $$x+(x+3)+(x+6)+(x+9)+(x+12)=50$$
$$\displaystyle \Rightarrow 5x+30=50\Rightarrow 5x=20\Rightarrow x=4$$
$$\displaystyle \therefore $$ Age of the youngest child is $$4$$ years.
Question 10
1 / -0

A number is doubled and 9 is added If the result is trebled it becomes 75 What is that number?

A
3.5

B
6

C
8

D
7

Solution

Let the number be x
According to the question
3 ( 2x + 9) = 75 $$\displaystyle \Rightarrow $$ 6x + 27 = 75
$$\displaystyle \Rightarrow $$ 6x = 75 - 27 = 48 $$\displaystyle \Rightarrow $$ x = 8

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 17

Result

Linear Equations in One Variable Test - 17

Score

-

Rank

-

SHARING IS CARING

Question 1

$$11$$ km

$$12$$ km

$$9$$ km

$$10$$ km

Solution

Question 2

$$10$$ and $$14$$

$$18$$ and $$20$$

$$16$$ and $$34$$

$$12$$ and $$29$$

Solution

Question 3

7

5

-7

3

Solution

Question 4

$$r+3=15$$

$$15-r=3$$

$$3r=15$$

$$\displaystyle \frac{3}{r}=15$$

Solution

Question 5

$$15$$

$$9.6$$

$$7.5$$

$$10$$

Solution

Question 6

$$2x + 3 = 7x - 2$$

$$\displaystyle \frac{2}{3}x + 5 = 3x - 4$$

$$\displaystyle x^2 + 3 = 5x - 3$$

$$\displaystyle (x - 2)^2 = x^2 + 8$$

Solution

Question 7

$$26 , 30, 34$$

$$24, 32, 34$$

$$24, 28, 38$$

$$28, 30, 32$$

Solution

Question 8

7 years

8 years

9 years

10 years

Solution

Question 9

4 years

8 years

10 years

6 years

Solution

Question 10

3.5

6

8

7

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.