Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

The sum of seven consecutive odd integer is $$133$$. The least integer is

A
$$17$$

B
$$19$$

C
$$11$$

D
$$13$$

Solution

Let the seven consecutive odd integers be
$$(2x+1),\:(2x+3),\:(2x+5),\:(2x+7),\:(2x+9),\:(2x+11),\:(2x+13)$$
Then, $$(2x+1)+(2x+3)+(2x+5)+(2x+7)+(2x+9)+(2x+11)+(2x+13)=133$$
$$\Rightarrow 14x+49=133$$
$$\Rightarrow \displaystyle 14x=133-49=84$$
$$\Rightarrow x=\dfrac{84}{14}=6$$
Hence, the least odd integer is $$=2x+1=2\times 6+1=13$$.
Question 2
1 / -0

4 is added to a number and the sum is multiplied by 5. If 20 is subtracted from the product and the difference is divided by 8 the result is equal to 10. Find the number.

A
$$16$$

B
$$12$$

C
$$8$$

D
$$20$$

Solution

Let, the number be $$x$$
A.T.Q,
$$ \dfrac{5(4+x)-20}{8}=10$$
$$\implies 5(4+x)-20=10 \times 8$$
$$\implies 20+5x=80+20$$
$$\implies 5x=100-20$$
$$\implies x=\dfrac{80}{5}=16$$
$$\therefore$$ the number is $$16$$
Question 3
1 / -0

One third of a pole is painted yellow one-fifth is painted white and the remaining 7 meters is painted black the length of the pole is

A
15 m

B
30 m

C
$$\displaystyle 10\frac{7}{15}$$ m

D
$$\displaystyle 7\frac{1}{15}$$ m

Solution

Let the total length of the pole be $$x$$
$$\displaystyle \frac{x}{3}+\frac{x}{5}+7=x$$
$$\displaystyle \Rightarrow \frac{5x+3x+105}{15}=x$$
$$\displaystyle \Rightarrow 8x+105 = 15x\Rightarrow 7x=105$$
$$\displaystyle \Rightarrow x=\frac{105}{7}=15$$
Question 4
1 / -0

The sum of three consecutive multiples of 3 is 72 What is the largest number?

A
21

B
24

C
27

D
36

Solution

Let the three consecutive multiples of 3 be 3x, 3(x + 1) and 3 ( x + 2), i.e. 3x + 3 and 3x + 6
Given, 3x +3x + 3 + 3x +6 = 72
$$\displaystyle \Rightarrow $$ 9x + 9 = 72 $$\displaystyle \Rightarrow $$ 9x=63 $$\displaystyle \Rightarrow $$ x =7
$$\displaystyle \therefore $$ Largest multiple of 3 = 3 (x + 2) =3 (7 + 2)
=3 x 9 = 27
Question 5
1 / -0

Ram weights $$25$$ kg more than Shyam. Their combined weight is $$325$$ kg. How much does Shyam weight?

A
$$150$$ kg

B
$$175$$ kg

C
$$200$$ kg

D
$$125$$ kg

Solution

Let Shyam's weight be $$x$$ kg.
Then, Ram's weight $$=(x+25)$$ kg
Given, the sum of their weights is $$325$$ kg. Then, we have
$$x+(x+25)=325$$
$$\Rightarrow 2x+25=325$$
$$\Rightarrow 2x=325-25=300$$
$$\Rightarrow \displaystyle x=\frac{300}{2}=150$$
$$\therefore $$ Shyam's weight $$=150$$ kg.
Question 6
1 / -0

Ramu's father is thrice as old as Ramu. If father's age is 45 years then Ramu's age is

A
$$45 $$years

B
$$30$$ years

C
$$15$$ years

D
$$10$$ years

Solution

Let, Ramu's age be $$x$$ years
$$\therefore$$ Ramu's father's age will be $$3x$$ years
Father's age is $$45$$
$$\therefore 3x=45$$
$$\implies x=\dfrac{45}{3}=15$$
$$\therefore$$ Ramu's age is $$ 15$$ years
Question 7
1 / -0

Shuba got three fourth of what Alka had, Alka gave half of what remained with her to Mohini If Mohini got Rs 625 how much did Alka have in the beginning?

A
Rs 3750

B
Rs 7000

C
Rs 5000

D
Rs 5625

Solution

Let Alka have Rs $$x$$ in the beginning
Amount that Shubha got $$\displaystyle =Rs\frac{3x}{4}$$
Amount remaining with Alka $$\displaystyle =x-\frac{3x}{4}=Rs\frac{x}{4}$$
Amount that mohini got = $$\displaystyle \frac{1}{2}\times\frac{x}{4}=Rs\frac{x}{8}$$
Given $$\displaystyle \frac{x}{8}=625\Rightarrow x=625\times8=Rs\, 5000$$
Question 8
1 / -0

In an examination, a student attempted $$15$$ questions correctly and secured $$40$$ marks. If there were two types of questions ($$2$$ marks and $$4$$ marks questions) how many questions of $$2$$ marks did he attempt correctly?

A
$$5$$

B
$$10$$

C
$$6$$

D
$$7$$

Solution

Let the number of $$2$$ marks question attempted correctly be $$x$$
Then the number of $$4$$ marks questions attempted correctly $$= ( 15 - x)$$
Total marks obtained= $$40$$
So,
$$x \times 2 + (15 - x ) \times 4 = 40$$
$$\displaystyle \Rightarrow 2x + 60 - 4x = 40$$
$$\Rightarrow -2x=-20$$
Hence, $$x=10$$.
Question 9
1 / -0

Ramu's father is thrice as old as Ramu. If father's age is $$45$$ years, then Ramu's age is

A
$$45$$ yrs

B
$$30$$ yrs

C
$$15$$ yrs

D
$$10$$ yrs

Solution

Let Ramu's father's age be $$3x$$ and Ramu's age be $$x$$.
Father's age is $$45$$ years.
Then, $$3x= 45$$
$$\Rightarrow x\, =\, \displaystyle \frac {45}{3}\, =\, 15$$
$$\therefore$$ Ramu's age $$= 15$$ yrs.
Question 10
1 / -0

A number is multiplied by $$6$$ and $$12$$ is added to the product. The result is $$84$$. Then the number is:

A
$$-12$$

B
$$72$$

C
$$+12$$

D
$$-72$$

Solution

Let the number be $$x$$
Then, $$x \times 6 + 12 = 84$$
$$\Rightarrow 6x = 84 -12 = 72$$
$$\Rightarrow x\, =\, \displaystyle \frac {72}{6}\, =\, 12$$
Hence required number is $$x=12$$

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Linear Equations in One Variable Test - 18

Result

Linear Equations in One Variable Test - 18

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Question 1

$$17$$

$$19$$

$$11$$

$$13$$

Solution

Question 2

$$16$$

$$12$$

$$8$$

$$20$$

Solution

Question 3

15 m

30 m

$$\displaystyle 10\frac{7}{15}$$ m

$$\displaystyle 7\frac{1}{15}$$ m

Solution

Question 4

21

24

27

36

Solution

Question 5

$$150$$ kg

$$175$$ kg

$$200$$ kg

$$125$$ kg

Solution

Question 6

$$45 $$years

$$30$$ years

$$15$$ years

$$10$$ years

Solution

Question 7

Rs 3750

Rs 7000

Rs 5000

Rs 5625

Solution

Question 8

$$5$$

$$10$$

$$6$$

$$7$$

Solution

Question 9

$$45$$ yrs

$$30$$ yrs

$$15$$ yrs

$$10$$ yrs

Solution

Question 10

$$-12$$

$$72$$

$$+12$$

$$-72$$

Solution

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