MCQ Questions for Class 8 Maths: Ch 2 Linear Equations in One Variable

 

1. David cuts a bread into two equal pieces and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If he has seven pieces of the bread all with him, how heavy is the original cake.

(a) 120 gm

(b) 180 gm

(c) 300 gm

(d) 240 gm

► (d) 240 gm

2. Mary was counting down from 34 and Thomas was counting upwards simultaneously, the number starting from 1 and he was calling out only the odd numbers. Which common number will they call out at the same time if they were calling out at the same speed?

(a) 20

(b) 21

(c) 22

(d) 23

► (d) 23

3. Find the solution of 2x – 3 = 7 

(a) 3

(b) 4

(c) 5

(d) none of these

► (c) 5

4. The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.   

(a) 4/12       

(b) 3/13       

(c) 3/7   

(d) 11/7

► (c) 3/7   

5. Solve 2x − 3 = x + 2

(a) 4

(b) 5

(c) 3

(d) 0

► (b) 5

6. In the following number sequence, how many such even numbers are there which are exactly divisible by its immediate preceding number but not exactly divisible by its immediate following number?

3  8  4  1  5  7  2  8  3  4  8  9  3  9  4  2  1  5  8  2

(a) One

(b) Two

(c) Three

(d) Four

► (b) Two

7. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

(a) 2

(b) 3

(c) 4

(d) none of these

► (c) 4

8. The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.

(a) 112

(b) 126

(c) 119

(d) 116

► (a) 112

9. Solve: 5x−2(2x−7)=(3x−1)+7/2

(a) 2

(b) 3

(c) 1/2

(d) 23/4

► (d) 23/4

10. The distance between two mile stones is 230 km and two cars start simultaneously from the milestones in opposite directions and the distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/h, find the speed of each car.

(a) 25 km/h, 40 km/h

(b) 40 km/h, 50 km/h

(c) 20 km/h, 40 km/h

(d) 30 km/h, 40 km/h

► (d) 30 km/h, 40 km/h

11. The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. What are the two numbers?

(a) 22 and 88

(b) 44 and 66

(c) 44 and 110

(d) 33 and 99

► (c) 44 and 110

12. In an equation the values of the expressions on the LHS and RHS are _______.

(a) different

(b) not equal

(c) equal

(d) none of these

► (c) equal

13. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

(a) 85

(b) 58

(c) 36

(d) 76

► (a) 85

14. Solve 2y + 9 = 4.

(a) -5/2

(b) 1/2

(c) 2

(d) none of these

► (a) -5/2

15. Solve: 7x = 21

(a) 3

(b) 2

(c) 14

(d) none of these

► (a) 3

16. An MNC company employed 25 men to do the official work in 32 days. After 16 days, it employed 5 more men and work was finished one day earlier. If it had not employed additional men, it would have been behind by how many days?

(a) 1 day

(b) 2 days

(c) 3 days

(d) 2.5 days

► (b) 2 days

17. The sum of two digit number and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.       

(a) 46       

(b) 48       

(c) 64  

(d) 84

► (c) 64

18. Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake ?

(a) 120 gm

(b) 180 gm

(c) 300 gm

(d) 240 gm

► (d) 240 gm

19. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

(a) 40 and 60

(b) 50 and 55

(c) 50 and 60

(d) 40 and 55

► (d) 40 and 55

20. Solve: y + 3 = 10

(a) 13

(b) 7

(c) -7

(d) none of these

► (b) 7

21. Solve: 3x = 12

(a) 15

(b) 4

(c) 9

(d) 3

► (b) 4

22. What will be the solution of these equations ax+by = a-b, bx-ay = a+b       

(a) x = 1, y = 2

(b) x = 2,y = -1

(c) x = -2, y = -2

(d) x = 1, y = -1

► (d) x = 1, y = -1

Linear Equations in One Variable Class 8 Extra important Questions Very Short Answer Type

Question 1.
Identify the algebraic linear equations from the given expressions.
(a) x² + x = 2
(b) 3x + 5 = 11
(c) 5 + 7 = 12
(d) x + y² = 3
Solution:
(a) x² + x = 2 is not a linear equation.
(b) 3x + 5 = 11 is a linear equation.
(c) 5 + 7 = 12 is not a linear equation as it does not contain variable.
(d) x + y² = 3 is not a linear equation.

Question 2.
Check whether the linear equation 3x + 5 = 11 is true for x = 2.
Solution:
Given that 3x + 5 = 11
For x = 2, we get
LHS = 3 × 2 + 5 = 6 + 5 = 11
LHS = RHS = 11
Hence, the given equation is true for x = 2

Question 3.
Form a linear equation from the given statement: ‘When 5 is added to twice a number, it gives 11.’
Solution:
As per the given statement we have
2x + 5 = 11 which is the required linear equation.

Question 4.
If x = a, then which of the following is not always true for an integer k. (NCERT Exemplar)
(a) kx = ak
(b) xk = ak
(c) x – k = a – k
(d) x + k = a + k
Solution:
Correct answer is (b).

h

Question 5.
Solve the following linear equations:
(a) 4x + 5 = 9
(b) x + 32 = 2x
Solution:
(a) We have 4x + 5 = 9
⇒ 4x = 9 – 5 (Transposing 5 to RHS)
⇒ 4x = 4
⇒ x = 1 (Transposing 4 to RHS)
(b) We have x + 32 = 2x
⇒ 32 = 2x – x
⇒ x = 321

Question 6.
Solve the given equation 31x × 514 = 1712
Solution:
We have 31x × 514 = 1712

3

Question 7.
Verify that x = 2 is the solution of the equation 4.4x – 3.8 = 5.
Solution:
We have 4.4x – 3.8 = 5
Putting x = 2, we have
4.4 × 2 – 3.8 = 5
⇒ 8.8 – 3.8 = 5
⇒ 5 = 5
L.H.S. = R.H.S.
Hence verified.

Question 8.

Solution:

⇒ 3x × 3 – (2x + 5) × 4 = 5 × 6
⇒ 9x – 8x – 20 = 30 (Solving the bracket)
⇒ x – 20 = 30
⇒ x = 30 + 20 (Transposing 20 to RHS)
⇒ x = 50
Hence x = 50 is the required solution.

Question 9.
The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles of the triangle.
Solution:
Let the angles of a given triangle be 2x°, 3x° and 4x°.
2x + 3x + 4x = 180 (∵ Sum of the angles of a triangle is 180°)
⇒ 9x = 180
⇒ x = 20 (Transposing 9 to RHS)
Angles of the given triangles are
2 × 20 = 40°
3 × 20 = 60°
4 × 20 = 80°

Question 10.
The sum of two numbers is 11 and their difference is 5. Find the numbers.
Solution:
Let one of the two numbers be x.
Other number = 11 – x.
As per the conditions, we have
x – (11 – x) = 5
⇒ x – 11 + x = 5 (Solving the bracket)
⇒ 2x – 11 = 5
⇒ 2x = 5 + 11 (Transposing 11 to RHS)
⇒ 2x = 16
⇒ x = 8
Hence the required numbers are 8 and 11 – 8 = 3.

Question 11.
If the sum of two consecutive numbers is 11, find the numbers.
Solution:
Let the two consecutive numbers be x and x + 1.
As per the conditions, we have
x + x + 1 = 11
⇒ 2x + 1 = 11
⇒ 2x = 11 – 1 (Transposing 1 to RHS)
⇒ 2x = 10
x = 5
Hence, the required numbers are 5 and 5 + 1 = 6.

Linear Equations in One Variable Class 8 Extra Questions Short Answer Type

Question 12.
The breadth of a rectangular garden is 23 of its length. If its perimeter is 40 m, find its dimensions.
Solution:
Let the length of the garden be x m
its breadth = 23 × m.
Perimeter = 2 [length + breadth]

Question 13.
The difference between two positive numbers is 40 and the ratio of these integers is 1 : 3. Find the integers.
Solution:
Let one integer be x.
Other integer = x – 40
As per the conditions, we have
x−40x = 13
⇒ 3(x – 40) = x
⇒ 3x – 120 = x
⇒ 3x – x = 120
⇒ 2x = 120
⇒ x = 2
Hence the integers are 60 and 60 – 40 = 20.

Question 14.
Solve for x:

Solution:

Question 15.
The sum of a two-digit number and the number obtained by reversing its digits is 121. Find the number if it’s unit place digit is 5.
Solution:
Unit place digit is given as 5
Let x be the tens place digit
Number formed = 5 + 10x
Number obtained by reversing the digits = 5 × 10 + x = 50 + x
As per the conditions, we have
5 + 10x + 50 + x = 121
⇒ 11x + 55 = 121
⇒ 11x = 121 – 55 (Transposing 55 to RHS)
⇒ 11x = 66
⇒ x = 6
Thus, the tens place digit = 6
Hence the required number = 5 + 6 × 10 = 5 + 60 = 65