Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

The sum of four consecutive odd positive integers is $$160$$. Find the largest among them.

A
37

B
39

C
41

D
43

E
45

Solution

Let the four consecutive odd positive integers are $$x,x+2,x+4,x+6$$
$$\therefore x+x+2+x+4+x+6=160$$
$$ 4x+12=160$$
$$ 4x=160-12$$
$$ 4x=148$$
$$x=\dfrac{148}{4}$$
$$=37$$
$$\therefore $$ Largest odd integer is $$37+6=43$$.
Question 2
1 / -0

If the number of boys in a class is thrice the number of girls and the total number of boys is 84, calculate the number of girls in the class.

A
$$28$$

B
$$20$$

C
$$30$$

D
$$252$$

Solution

Let the number of girls are $$x$$
Then number of boys $$=3x$$
$$\Rightarrow 3x=84$$
$$\Rightarrow x=\dfrac{84}{3}=28$$
Then number of girls $$=28$$
Question 3
1 / -0

The sum of five positive, consecutive integers is $$115$$. Find the value of the smallest integer among these.

A
$$21$$

B
$$22$$

C
$$23$$

D
$$24$$

E
$$25$$

Solution

Let the five consecutive integers are $$x,x+1,x+2,x+3,x+4$$
$$\therefore x+x+1+x+2+x+3+x+4=115$$
$$\Rightarrow 5x+10=115$$
$$\Rightarrow 5x=115-10$$
$$\Rightarrow 5x=105$$
$$\Rightarrow x=\dfrac{105}{5}=21$$
The smallest integer $$=21$$
Question 4
1 / -0

If $$\dfrac{2}{3}(5x+7)=8x$$,then $$x$$ is equal to:

A
$$1$$

B
$$0$$

C
$$2$$

D
$$-2$$

Solution

Given, $$ \dfrac{2}{3}(5x+7)=8x$$.

$$\Rightarrow \dfrac{10x}{3}+\dfrac{14}{3}=8x$$ ...[By Distribution Law]

$$\Rightarrow \dfrac{10x+14}{3}=8x$$ …[Cross-multiplying the denominators on the LHS]

$$\Rightarrow 10x+14=24x$$ ...[Multiplying $$3$$ on both sides].

Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 10x-24x=-14$$

$$\Rightarrow -14x=-14$$

$$\Rightarrow x=\dfrac{-14}{-14}=1$$.

Hence, option $$A$$ is correct.
Question 5
1 / -0

A club has $$27$$ employees. If there are seven more women than men in the club, calculate the number of men in the club.

A
$$10$$

B
$$8$$

C
$$6$$

D
$$9$$

Solution

Let the number of men in the club $$=x$$
Then number of women $$=$$ $$x+7$$
Then according to the question,
$$\Rightarrow x+x+7=27$$
$$\Rightarrow 2x=27-7$$
$$\Rightarrow 2x=20$$
$$\Rightarrow x=\dfrac{20}{2}=10$$
Then number of men $$=10$$
Question 6
1 / -0

$$280$$ meals are to be prepared by three chefs. Every chef has its own speed but the combined output of all three is modelled by the equation $$8x+4x+2x=280$$. If $$x$$ is a positive integer, which of the following could $$8x$$ represent in the equation?

A
The total meal output by the slowest chef, who made $$40$$ meals

B
The total meal output by the fastest chef, who made $$160$$ meals

C
The total meal output by the fastest chef, who made $$80$$ meals

D
The different between the output between the slowest and fastest chef, which would be $$120$$ meals

Solution

In given equation $$8x+4x+2x=280$$
Then $$14x=280$$
$$\therefore x=20$$
Then $$x$$ is $$20$$ meals
Then mean of $$8x$$ in equation is
$$8x=8\times 20=160$$ meals
Then the meal output by the fastest chef, who made $$160$$ meals.
Question 7
1 / -0

The value of $$d$$ which satisfies the expression $$\cfrac{4(d+3)-9}{8}=\cfrac{10-(2-d)}{6}$$ is:

A
$$\cfrac{23}{16}$$

B
$$\cfrac{23}{8}$$

C
$$\cfrac{25}{8}$$

D
$$\cfrac{25}{4}$$

Solution

Given, $$\dfrac {4(d+3)-9}{8}=\dfrac {10-
(2-d)}{6}$$.

Cross multiplying, we get,
$$24(d+3)-54=80-8(2-d)$$

$$\Rightarrow 24d+72-54=80-16+8d$$ ...[By Distribution Law]

$$\Rightarrow 24d+18=64+8d$$.

Transposing $$d$$ terms to one side, we get,
$$\Rightarrow 24d-8d=64-18$$

$$\Rightarrow 16d=46$$

$$\Rightarrow d=\dfrac{23}{8}$$.

Hence, option $$B$$ is correct.
Question 8
1 / -0

Consider two consecutive positive integers. It is given that the result of adding the smaller integer and triple the larger integer is $$79$$. Find the $$2$$ integers.

A
18, 19

B
19, 20

C
20, 21

D
26, 27

E
39, 40

Solution

Let the two consecutive positive integers are $$x,x+1$$
The according to the question,
$$\Rightarrow x+3(x+1)=79$$
$$\Rightarrow x+3x+3=79$$
$$\Rightarrow 4x=79-3$$
$$\Rightarrow 4x=76$$
$$\Rightarrow x=\dfrac{76}{4}=19$$
Another integer $$=19+1=20$$
So, the two integers are $$19,20$$.
Question 9
1 / -0

The sum of three consecutive integers is equal to $$192$$. What is the product of these numbers?

A
$$216000$$

B
$$7077888$$

C
$$576$$

D
$$110592$$

E
$$262080$$

Solution

Let the three consecutive numbers be $$x,x+1,x+2$$.
To get the three consecutive numbers whose sum is $$192$$, we get the equation as,
$$x+\left( x+1 \right) +\left( x+2 \right) =192$$
$$3x+3=192$$
$$3x=192-3$$ $$= 189$$
$$x=\dfrac { 189 }{ 3 } $$
$$x=63$$
So the first number out of the three consecutive numbers is $$63$$,
The three numbers are $$63,64$$ and $$65$$.

The product of these numbers is,
$$63\times 64\times 65=262080$$
Hence the correct answer is option E.
Question 10
1 / -0

When a number $$x$$ is subtracted from $$36$$ and then the difference is divided by $$x$$, the result is $$2$$. Find the value of $$x$$.

A
$$2$$

B
$$4$$

C
$$6$$

D
$$12$$

Solution

Let the number be $$x$$.

According to the question:

$$ \dfrac { 36-x }{ x } =2\\ \Rightarrow 36-x=2x\\ \Rightarrow 36=3x$$
$$ \Rightarrow x=12$$

Hence option (D) is correct option

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 38

Result

Linear Equations in One Variable Test - 38

Score

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SHARING IS CARING

Question 1

37

39

41

43

45

Solution

Question 2

$$28$$

$$20$$

$$30$$

$$252$$

Solution

Question 3

$$21$$

$$22$$

$$23$$

$$24$$

$$25$$

Solution

Question 4

$$1$$

$$0$$

$$2$$

$$-2$$

Solution

Question 5

$$10$$

$$8$$

$$6$$

$$9$$

Solution

Question 6

The total meal output by the slowest chef, who made $$40$$ meals

The total meal output by the fastest chef, who made $$160$$ meals

The total meal output by the fastest chef, who made $$80$$ meals

The different between the output between the slowest and fastest chef, which would be $$120$$ meals

Solution

Question 7

$$\cfrac{23}{16}$$

$$\cfrac{23}{8}$$

$$\cfrac{25}{8}$$

$$\cfrac{25}{4}$$

Solution

Question 8

18, 19

19, 20

20, 21

26, 27

39, 40

Solution

Question 9

$$216000$$

$$7077888$$

$$576$$

$$110592$$

$$262080$$

Solution

Question 10

$$2$$

$$4$$

$$6$$

$$12$$

Solution

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