Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

The sum of two consecutive natural numbers is $$23$$. Numbers will be-

A
$$11$$ and $$12$$

B
$$11$$ and $$14$$

C
$$11$$ and $$16$$

D
$$11$$ and $$18$$

Solution

Let the two consecutive natural numbers be $$x$$ and $$x+1$$
Now, according to the problem
$$x+(x+1)=23$$
$$\Rightarrow$$ $$2x+1=23$$
$$\Rightarrow$$ $$2x=23-1$$
$$\Rightarrow$$ $$2x=22$$
$$\Rightarrow$$ $$x=\cfrac{22}{2}=11$$
The one number is $$11$$
The next number is $$x+1=11+1=12$$
Hence the numbers are $$11$$ and $$12$$
Question 2
1 / -0

If $$\displaystyle \frac{2}{3}$$ of a number is $$20$$ less than the original number, then the number is

A
$$60$$

B
$$40$$

C
$$80$$

D
$$120$$

Solution

Let the number be $$x$$.

It is given that $$\dfrac {2}{3}$$ of a number, i.e. $$\dfrac {2}{3}x$$,
$$20$$ less than the original number, i.e. $$x-20$$.

The expression can be written as,

$$\displaystyle \frac{2}{3} x = x - 20$$
$$\therefore x = 60$$

Therefore, the number is $$60$$.
Question 3
1 / -0

Solve : $$10(2+x) = 5(x-6)$$

A
$$x = 3$$

B
$$x= -8$$

C
$$x = -10$$

D
$$x = 2$$

Solution

Given, $$10(2+x) = 5(x-6)$$
or, $$20 + 10x = 5x - 30$$
Transposing 5x to LHS, we get
$$20 + 10x - 5x = -30$$
Transposing 20 to RHS, we get
$$5x = -30 -20$$
or $$5x = -50$$
Dividing both sides by 5, we get
$$\displaystyle \frac{5x}{5} = \frac{-50}{5}$$ or $$x = -10$$
Question 4
1 / -0

Two cats Billy and Kitty together catch $$60$$ mice. If Billy catches three mice for every two caught by Kitty, then the number of mice caught by Kitty is

A
$$24$$

B
$$30$$

C
$$36$$

D
$$40$$

Solution

Ratio of number of mice caught by Billy and Kitty $$=3 : 2$$.
Let, the number of mice be $$3x$$ and $$2x$$

Therefore,
$$3x+2x=60$$
$$\Rightarrow 5x=60$$
$$\Rightarrow x=\dfrac {60}{5}$$
$$\Rightarrow x=12$$

Hence, number of mice caught by Kitty $$=2x$$
$$=2\times 12$$
$$=24$$
Question 5
1 / -0

A bag contains Rs. 90 in coins. If coins of 50 paise, 25 paise and 10 paise are in te ratio 2 : 3 : 5, then the number of 25 paise coins in the bag are

A
120

B
130

C
135

D
140

Solution

Let the number of 50 paise ,25 paise,10paise coins be 2x,3x and 5x.
Then the sum of their values$$=(\dfrac{50\times 2x}{100}+\dfrac{25\times 3x}{100}+\dfrac{10\times 5x}{100})$$
$$\Rightarrow x+\dfrac{3x}{4}+\dfrac{x}{2}=\dfrac{9x}{4}$$
$$\therefore \dfrac{9x}{4}=90$$
$$\Rightarrow x=\dfrac{90\times 4}{9}=40$$
Hence the number of 25 paise coins=$$3x=3\times 40=120$$
Question 6
1 / -0

If $$12 x = 4(x+3)$$, then $$x$$ equals:

A
$$1.5$$

B
$$\cfrac{3}{8}$$

C
$$5$$

D
$$\cfrac{12}{11}$$

Solution

Given, $$12 x = 4(x+3)$$.
$$\Rightarrow 12x=4x+12$$ ...[By Distribution Law].

Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 12x-4x=12$$
$$\Rightarrow 8x=12$$
$$\Rightarrow x=\cfrac{12}{8}=\cfrac{3}{2}=1.5$$.

Hence, option $$A$$ is correct.
Question 7
1 / -0

The difference between a number and one-fifth of it is $$100$$. What is the number?

A
$$125$$

B
$$200$$

C
$$225$$

D
$$300$$

Solution

Let the number is $$x$$
Then one fifth of $$x=$$ $$\dfrac{x}{5}$$
Given in question the difference of number and one fifth of number is $$100$$.
$$\therefore x-\dfrac{x}{5}=100$$
$$\Rightarrow 5x-x=500$$
$$\Rightarrow 4x=500$$
$$\Rightarrow x=125$$
Question 8
1 / -0

Find the value of $$t$$, if $$8+2t=18t-7$$.

A
$$\dfrac{16}{15}$$

B
$$\dfrac{-16}{15}$$

C
$$\dfrac{-15}{16}$$

D
$$\dfrac{15}{16}$$

Solution

Given, $$\displaystyle 8+2t=18t-7$$.

Transposing $$t$$ terms to one side, we get,
$$\Longrightarrow\displaystyle 8+7=18t-2t$$

$$\Longrightarrow \displaystyle 16t=15$$

$$\Longrightarrow\displaystyle t=\dfrac{15}{16}$$.

Hence, option $$D$$ is correct.
Question 9
1 / -0

Half of a number is added to $$18$$ then the sum is $$46$$. The number is

A
$$92$$

B
$$56$$

C
$$65$$

D
$$0$$

Solution

Let the number be $$x$$

According to the question,

$$\Rightarrow \displaystyle \frac{x}{2}\, +\, 18\, =\, 46$$

$$\Rightarrow \displaystyle \frac{x}{2}\, =\, 46\, -\, 18\, =\, 28$$

$$\Rightarrow x =28 \times 2\, $$

$$=\, 56$$
Question 10
1 / -0

If four times a number is 60 then the number is

A
1

B
15

C
60

D
-15

Solution

Let, the no. be $$x$$.
Acc. to question,
$$4x = 60 $$

$$x =$$ $$\displaystyle{\frac{60}{4}}=15$$

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 20

Result

Linear Equations in One Variable Test - 20

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SHARING IS CARING

Question 1

$$11$$ and $$12$$

$$11$$ and $$14$$

$$11$$ and $$16$$

$$11$$ and $$18$$

Solution

Question 2

$$60$$

$$40$$

$$80$$

$$120$$

Solution

Question 3

$$x = 3$$

$$x= -8$$

$$x = -10$$

$$x = 2$$

Solution

Question 4

$$24$$

$$30$$

$$36$$

$$40$$

Solution

Question 5

120

130

135

140

Solution

Question 6

$$1.5$$

$$\cfrac{3}{8}$$

$$5$$

$$\cfrac{12}{11}$$

Solution

Question 7

$$125$$

$$200$$

$$225$$

$$300$$

Solution

Question 8

$$\dfrac{16}{15}$$

$$\dfrac{-16}{15}$$

$$\dfrac{-15}{16}$$

$$\dfrac{15}{16}$$

Solution

Question 9

$$92$$

$$56$$

$$65$$

$$0$$

Solution

Question 10

1

15

60

-15

Solution

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