## Linear Equations In One Variable

**Class 8 Maths**

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*Q & A based on Class 8 NCERT Chapter *

**Q1(MCQ): If 3x – 4 (64 – x) = 10, then the value of x is**

(a) –266

(b) 133

(c) 66.5

(d) 38

Answer: (d)38

3x - 256 + 4x =10

7x = 10 + 256 = 266

x = 266/7 = 38

**Q2: Three consecutive even numbers whose sum is 156 are 51, 52 and 53.**

**State if the above statement is True or False**

Answer: False

Let the three consecutive even numbers be x, x+2, x+4

∴ x + x+ 2 + x+4 = 156

⇒ 3x + 6 = 156

⇒ 3x = 156 - 6 = 150

⇒ x = 150 / 3 = 50

Thus numbers are 50, 51, 52

**Q3: Fifteen added to thrice a whole number gives 93. The number is __________.**

Answer: 26

**Q4: x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21+x (True or False)**

Answer: True

For x = -12,

LHS = 5(-12) -3[2(-12) + 1] = -60 -3[-24+ 1] = -60 -3(23) = -60 + 69 = 9

RHS = 21 + (-12) = 21 - 12 = 9

Thus LHS = RHS

**Q5: The present age of a father is four times the age of his son. After 10 years, the age of father will become three times the age of his son. Find their present ages.**

Answer: Let the present age of son be x years

∴ The present age of father = 4x years

After 10 years,

Age of son = (x + 10) years

Age of father = (4x + 10) years

According to the given condition

4x + 10 = 3(x + 10)

4x + 10 = 3x + 30

4x – 3x = 30 –10

x = 20

∴ Present age of son = 20 years.

and present age of father = 4x = 4 × 20 = 80 years.

**Q6(MCQ): If 8x – 3 = 25 +17x, then x is**

(a) a fraction

(b) an integer

(c) a rational number

(d) cannot be solved

Answer: (c) a rational number

8x - 3 = 25 + 17x

On transposing,

8x - 17x = 25 + 3

-9x = 28

x = -28/9 which is a rational number.

**Q7(MCQ): The shifting of a number from one side of an equation to other is called**

(a) Transposition

(b) Distributivity

(c) Commutativity

(d) Associativity

Answer: (a) Transposition

**Q8(MCQ): A linear equation in one variable has**

(a) Only one solution

(b) Two solutions

(c) More than two solutions

(d) No solution

Answer: (a) Only one solution

**Q9(MCQ): The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.**

(a) 112

(b) 126

(c) 119

(d) 116

Answer: (a) 112

Let the numbers be x, x+7, x+14

∴ x + x + 7 + x + 14 = 357

⇒ 3x + 21 = 357

⇒ 3x = 357 - 21 = 336

⇒ x 336 / 3 = 112

**Q10: The solution of the equation 3x – 4 = 1 – 2 x is _________.**

Answer: 1

**Q11: In a linear equation, the _________ power of the variable appearing in the equation is one.**

Answer: highest

**Q12: Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.**

Answer: ₹ 4500

Let Kiran gets = ₹p

Salma gets - ₹p + 1000

Jenifer gets = ₹p + 500

∴ Sum is p + p + 1000 + p + 500 = 13500

⇒ 3p = 13500 - 1500 = 12000

⇒ p = 12000/3 = 4000

∴ Jenifer gets = 4000 + 500 = ₹ 4500

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ReplyDeleteanswer of question 4 is wrong

ReplyDeleteThanks Ojas for finding the error. It has been corrected. Thanks.

DeleteThis actually not a a type of m. C.q. in m. C. Q there r basic concepts so you should post another m. C. Q

Deletethe answer is still not corrected

ReplyDeleteTypo corrected in Q4.

Deleteno it is right

ReplyDeletethen what is the correct answer

ReplyDelete