Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

What should be subtracted from $$\displaystyle\left(\displaystyle\frac{3}{4}-\frac{2}{3}\right)$$ to get $$\displaystyle\frac{-1}{6}$$?

A
$$\displaystyle -\frac{6}{13}$$

B
$$\displaystyle\frac{1}{4}$$

C
$$\displaystyle\frac{2}{7}$$

D
$$\displaystyle -\frac{1}{8}$$

Solution

From the given question, we can write that

$$\dfrac{3}{4} - \dfrac{2}{3} -a = -\dfrac{1}{6}$$

We have to find $$a$$

$$a=\dfrac{3}{4}-\dfrac{2}{3}+ \dfrac{1}{6}$$

$$a=\dfrac{3 \times 3 - 2 \times 4 + 1 \times 2}{12}$$

$$a=\dfrac{9-8+2}{12}$$

$$a=\dfrac{3}{12}$$

$$a=\dfrac{1}{4}$$
Question 2
1 / -0

Solve for $$x$$:
$$\dfrac {9x}{7-6x}=15$$

A
$$\dfrac{99}{105}$$

B
$$-\dfrac{105}{99}$$

C
$$\dfrac{105}{99}$$

D
$$-\dfrac{99}{105}$$

Solution

$$\dfrac{9x}{7 - 6x} = 15$$

$$9x = 15(7 - 6x) = 105 - 90x$$

$$9x + 90x = 105 $$

$$99x = 105$$

$$x = \dfrac{105}{99}$$
Question 3
1 / -0

The sum of three consecutive multiples of $$11$$ is $$363$$. Find these multiples.

A
$$110,121,132$$

B
$$99,77,187$$

C
$$110,99,154$$

D
none

Solution

Let the three consecutive multiples of $$11$$ are $$11x,$$ $$11x+11$$ and $$11x+22$$

Their sum is $$363$$

$$11x+11x+11+11x+22=363$$

$$33x+33=363$$

$$33x=363-33$$

$$33x=330$$

$$x=\dfrac{330}{33}$$

$$x=10$$

First multiple $$=11x=11\times 10=110$$
Second multiple $$=11x+11=110+11=121$$
Third multiple $$=11x+22=110+22=132$$
Question 4
1 / -0

One-third of one half of one-fifth of a number is $$15$$ then the number is

A
$$50$$

B
$$150$$

C
$$15$$

D
$$450$$

Solution

Let the no. is $$x$$

One-third of one half of one fifth of $$x$$ is $$15$$

That is,

$$\dfrac{1}{3}$$ of $$\dfrac{1}{2}$$ of $$\dfrac{1}{5}$$ of $$x=15$$

$$\dfrac{1}{3}\times \dfrac{1}{2}\times \dfrac{1}{5}\times x=15$$

$$\dfrac{1}{30}\times x=15$$

$$x=15\times 30=450$$
Question 5
1 / -0

If $$ \cfrac { 5.6(x+3) }{ 0.7 } =24, $$ then the value of $$x$$ is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

$$ 5.6\dfrac{(x+3)}{0.7}=24 $$

$$ 5.6x+16.8=16.8 $$

$$ x=0 $$
Question 6
1 / -0

If $$\sqrt { 1+\dfrac { x }{ 289 } } =1\dfrac { 1 }{ 17 }$$ then $$x=$$

A
$$1$$

B
$$13$$

C
$$35$$

D
$$15$$

Solution

We have,

$$\sqrt{1+\dfrac{x}{289}}=1\dfrac{1}{17}$$

$$\sqrt{\dfrac{289+x}{289}}=\dfrac{18}{17}$$

On squaring both sides, we get

$$ {{\left( \sqrt{\dfrac{289+x}{289}} \right)}^{2}}={{\left( \dfrac{18}{17} \right)}^{2}} $$

$$ \dfrac{289+x}{289}=\dfrac{324}{289} $$

$$ 289+x=324 $$

$$ x=324-289 $$

$$ x=35 $$
Question 7
1 / -0

Find three consecutive numbers whose sum is $$108$$.

A
$$35, 46, 37$$

B
$$5, 36, 37$$

C
$$35, 36, 37$$

D
None of these

Solution

Let, the three consecutive numbers be $$x-1, x, x+1.$$

According to question,
$$x-1 + x + x+1 = 108$$
$$\Rightarrow 3x = 108$$
$$\Rightarrow x = \dfrac{108}{3}$$
$$\Rightarrow x =36$$

Hence, the required numbers are, $$35, 36, 37.$$
Question 8
1 / -0

Solve for $$x$$:-
$$\dfrac{{2x - 1}}{2}\,\,\, - \dfrac{{x + 3}}{3}\,\, = \dfrac{{x - 2}}{5}$$

A
$$x=\dfrac{5}{14}$$

B
$$x=\dfrac{3}{14}$$

C
$$x=\dfrac{33}{14}$$

D
None of these

Solution

$$\dfrac{{2x - 1}}{2}\,\,\, - \dfrac{{x + 3}}{3}\,\, = \dfrac{{x - 2}}{5}\Rightarrow \dfrac{6x-3-2x-6}{6}=\dfrac{x-2}{5}\Rightarrow 20x-45=6x-12\Rightarrow 14x=33\Rightarrow x=\dfrac{33}{14}$$
Question 9
1 / -0

If $$4$$ more than twice a number is $$6$$ less than that number then what is the number?

A
$$2$$

B
$$-10$$

C
$$10$$

D
$$16$$

Solution

Lets assume the number is $$x$$.
According to the question statement, we get $$4+2x=x-6$$
$$2x-x = -6-4$$.
$$x = -10$$.
Question 10
1 / -0

Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

A
65

B
36

C
72

D
74

Solution

Let the total no of deer be $$x$$

So, we have

$$ x - \left(\dfrac { 1 }{ 2 } x +\dfrac { 3 }{ 4 } \times \dfrac { 1 }{ 2 } x\right) =9\\ x-\left(\dfrac { 1 }{ 2 } x +\dfrac { 3 }{ 8 } x\right) =9\\ x-\dfrac { 7 }{ 8 } x =9\\ \dfrac { 1 }{ 8 } x =9; $$
Thus, $$x =72$$ deer in the herd.

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 24

Result

Linear Equations in One Variable Test - 24

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SHARING IS CARING

Question 1

$$\displaystyle -\frac{6}{13}$$

$$\displaystyle\frac{1}{4}$$

$$\displaystyle\frac{2}{7}$$

$$\displaystyle -\frac{1}{8}$$

Solution

Question 2

$$\dfrac{99}{105}$$

$$-\dfrac{105}{99}$$

$$\dfrac{105}{99}$$

$$-\dfrac{99}{105}$$

Solution

Question 3

$$110,121,132$$

$$99,77,187$$

$$110,99,154$$

none

Solution

Question 4

$$50$$

$$150$$

$$15$$

$$450$$

Solution

Question 5

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 6

$$1$$

$$13$$

$$35$$

$$15$$

Solution

Question 7

$$35, 46, 37$$

$$5, 36, 37$$

$$35, 36, 37$$

None of these

Solution

Question 8

$$x=\dfrac{5}{14}$$

$$x=\dfrac{3}{14}$$

$$x=\dfrac{33}{14}$$

None of these

Solution

Question 9

$$2$$

$$-10$$

$$10$$

$$16$$

Solution

Question 10

65

36

72

74

Solution

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