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# Test: Linear Equations- 1

## 10 Questions MCQ Test NCERT Mathematics for CAT Preparation | Test: Linear Equations- 1

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Attempt Test: Linear Equations- 1 | 10 questions in 10 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study NCERT Mathematics for CAT Preparation for Class 8 Exam | Download free PDF with solutions
QUESTION: 1

### 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 ?

Solution:

Seven pieces consist of 6 smaller equal pieces and one half cake piece.
Weight of each small piece = 20 gm
So, total weight of the cake = (20×6) = 120gm.
If one half is 120 gm, then so is the other. Therefore the total weight of the cake is 120*2= 240 gm.

QUESTION: 2

### Solve 2x − 3 = x + 2

Solution:

Given, 2x - 3 = x + 2
Transposing 'x' to L.H.S
⇒ 2x - x - 3 = 2
⇒ x - 3 = 2
Transposing '3' to R.H.S
⇒ x = 2 + 3
⇒ x = 5.
Therefore, option (b) is the correct answer.

QUESTION: 3

### 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.

Solution:

Let the numerator be x & denominator be y
Fraction = numerator/denominator = x/y
ATQ
CASE 1 :
x = y - 4
x- y = - 4 …………..(1)

CASE 2 :
8(x - 2) = y + 1
8x - 16 = y + 1
8x - y = 17………... (2)

On Subtracting equation (2) from (1)
x - y = - 4
8x - y = 17
(-) (+) (-)
----------------
-7x = -21
Transposing (-7) to R.H.S, we get
x = 21/7
⇒ x = 3
Put x = 3 in equation 1,
x - y = - 4
3 - y = - 4
y = 3 + 4 = 7
y = 7

Therefore, x = 3 and y = 7
⇒ Fraction = x/y = 3/7
Hence, the fraction is 3/7.

QUESTION: 4

Solve: 5x−2(2x−7) = 2(3x−1)+7/2

Solution:

Given equation is 5x−2(2x−7) = 2(3x−1)+7/2

after opening the brackets
5x-4x+14 = 6x-2+7/2
taking a to one side constants to other side
6x+4x-5x=14+2-7/2
or 5x = 16-7/2
or 5x = (37-7)/2
or 5x = 25/2

QUESTION: 5

Find the solution of 2x - 3 = 7

Solution:

Given, 2x-3=7
Transposing -3 to R.H.S
2x=7+3
⇒ 2x=10
Transposing '2' to R.H.S, we get
x=10/2
⇒ x=5.
Therefore, the correct option is c.

QUESTION: 6

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?

Solution:

Let the unit digit be x
Tens digit =  x+3
Therefore, the number formed = 10(x+3)+x ∵ Two digit no = 10 * tens digit + unit digit

When digits are interchanged i.e
Unit digit = x+3
Tens digit = x
Therefore, the number formed by interchanging the digits is
10x + x + 3
Now, According to question

⇒ 10 (x+3) + x + 10x + x + 3  =143
⇒  10x + 30 + 12x + 3 = 143
⇒  22x + 33 = 143
Transposing '33' to R.H.S, we get
22x = 143−33
⇒ 22x=110
Transposing '22' to L.H.S, we get
x=110/22
⇒ x=5

Therefore, Original number = 10(5+3) + 5 = 85

QUESTION: 7

Solve 2y + 9 = 4.

Solution:

Given, 2y + 9 =4
Transposing '9' to R.H.S, we get
2y = 4-9
⇒ 2y = -5
Therefore, y = -5/2
Hence, option 'A' is correct.

QUESTION: 8

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

Solution:

Let the two given numbers be 5x and 2x
According to question ,
5x - 2x = 66
3x = 66
Transposing '3' to R.H.S, we get
x = 66/3
⇒ x = 22

So, 2x = 2 x 22 = 44
& 5x = 5 x 22 = 110

Hence, Option 'C' is the Correct answer.

QUESTION: 9

An algebraic equation is an _________ involving variables.

Solution:

An algebraic equation is an equality involving variables.

QUESTION: 10

Solve: 3x = 12

Solution:

Given, 3x = 12
Transposing '3' to R.H.S, we get
x = 12/3
⇒ x = 4

or
Divide both sides by '3' to get the value of x
3x/3 = 12/3
⇒ x = 4

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