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This mock test of Test: Linear Equations- 2 for Class 8 helps you for every Class 8 entrance exam.
This contains 20 Multiple Choice Questions for Class 8 Test: Linear Equations- 2 (mcq) to study with solutions a complete question bank.
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students definitely take this Test: Linear Equations- 2 exercise for a better result in the exam. You can find other Test: Linear Equations- 2 extra questions,
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QUESTION: 1

Solve: 4y = 20

Solution:
4y = 20 y = 20/4 y = 5

QUESTION: 2

Solve: 3x = 2x+ 18

Solution:
3x=2x+18 3x-2x=18 (transposing) x= 18

QUESTION: 3

Solve: x = 4/5(x+10)

Solution:

x = 4/5*(x + 10)

=> x = 4x/5 + 8

=> x - 4x/5 = 8

=> (5x - 4x)/5 = 8

=> x = 8 * 5 = 40

Verification / Checking-

LHS = x = 40

RHS = 4/5*(x + 10) = 4/5*(40 + 10) = 4/5 * 50 = 40

QUESTION: 4

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

Solution:

QUESTION: 5

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

Solution:

QUESTION: 6

The sum of two digits 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.

Solution:

Let the unit digit be y & tens digit be x.

Original number = (10x+y)

After interchanging the digits

New number = (10y+x)

(10x+y) + (10y+x) = 110

11x +11y = 110

11(x+y)= 110

x+y = 110/11

x+y= 10 (1)

x= 10-y (2)

(10x+y) - 10 = 4+ 5(x+y)

(10x+y) - 10 = 4+ 5(10)

(10x+y) = 4+ 50+10

(10x+y) = 64

10(10-y) +y = 64

100-10y +y= 64

100 -9y = 64

-9y = 64-100

-9y = -36

y= 36/9= 4

y= 4

putting the value of y in eqn 2

x= 10-y

x= 10-4

x= 6

Hence , the first number is 6 & second number is 4.

Original Number is 10x+y = 10* 6+4= 60+4= 64

QUESTION: 7

Solve: x − 2 = 7

Solution:

QUESTION: 8

Solve: 5t – 3 = 3t – 5

Solution:

5t-3=3t-55t-3t=-5+32t=-2 which gives t=-1

QUESTION: 9

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

Solution:

ax+by=a-b

ax=a-b-by

x=(a-b-by)/a

bx-ay=a+b

substituting

b((a-b-by)/a)-ay=a+b

(ab-b²-b²y-a²y)/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

y=-(a²+b²)/(a²+b²)

y= -1

substituting value of y

x=(a-b-b(-1))/a

x=a/a

x=1

QUESTION: 10

The present age of Sahil’s mother is three times the present age of Sahil. After 5 years their ages will add to 66 years. Find their present ages.

Solution:

Let present age of sahil is 'x'

his mother age is '3x'

after five yearssahil's age is 'x+5'

his mother's age is '3x+5'

according to problem, given sum of their ages after five years is 66

⇒(x+5)+(3x+5)=66

4x+10=664x=66-10

4x=56

x=56/4

x=14sahil's age is x=14=14 years

sahil's mother age is 3x=3(14)= 42=42 years.

QUESTION: 11

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?

Solution:

Let she thoughts the no x

according to question ,she subtract the 5/2 from the no.= x-5/2

now ,she multiply the result by 8 =8(x-5/2)

according to statement

3x = 8(x-5/2)

3x=8x -20

20=5x

x=4

she thought the no. as 4

QUESTION: 12

Solve: 7x = 21

Solution:

QUESTION: 13

Solve: 5x+ 9 = 5 + 3x

Solution:

QUESTION: 14

Solve: y + 3 = 10

Solution:
Option B is correct bcoz...

y + 3 = 10

y = 10 - 3

y = 7

y + 3 = 10

y = 10 - 3

y = 7

QUESTION: 15

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

Solution:

Let the number be x.

So, the other number is (x + 15).

(x + 15) + x = 95

2x + 15 = 95

2x = 95 - 15

2x = 80

x = 40

So, the numbers are 40 and 55.

QUESTION: 16

The value of the expression on one side of the equality sign is _____ to the value of the expression on the other side.

Solution:

This says that any given equation says that it’s LHS is equal to RHS.

QUESTION: 17

Solution:
2x/3 + 1 = 7x/15 + 3
=> 2x/3 -- 7x/15 = 3 -- 1
=> 10x -- 7x/15 = 2
=> 3x/15 = 2
=> 3x = 2 × 15
=> 3x = 30
=> x = 30/3
=> x = 10

QUESTION: 18

Solve: 5a = 30

Solution:

QUESTION: 19

Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age. Find their present ages.

Solution:

Let Arjun's age be x and shriya's age be y

A.T.Q.

x=2y

x-5=3 (y-5)

=>x-5=3y-15

=>2y-3y=-15+5

=>-y=-10

=>y=10

Now ,

x=2y

=>x=(2x10)

=>x=20

Therefore Arjun's age is 20 yrs and Shriya's age is 10 yrs.

QUESTION: 20

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish the work in 14 days. find the time taking by 1 man alone and 1 boy alone to finish the same work.

Solution:

Let the time taken by man be x days

time taken by boys be y days

work done by 1 man in one day=1/x

work done by 1 boy in one day=1/y

8/x+12/y = 1/10 - eq 1

6/x+ 8/y = 1/14 - eq2

Let u = 1/x & v = 1/y

8u+ 12y = 1/10 - eq3

6u+8v = 1/14 - eq4

Multiplying eq3 by 2 & eq4 by 3

16u+ 24y = 2/10 - eq5

18u+24v = 3/14 - eq6

subtract eq 5 & 6

-2u = -3/14+2/10

-2u = (-3×10 +2×14)/140

-2u = (-30+28)/140

-2u = -2/140

u = 1/140

put this value in eq 5

16u+ 24y = 2/10

16×1/140 +24y = 1/5

4/35+24y = 1/5

24y = 1/5-4/35

24y = (1×7-4)/35

24y = (7-4)/35

24y = 3/35

y= 3/35×24

y= 1/280

u=1/x

1/140 = 1/x

x = 140

v = 1/y

1/280 = 1/y

y = 280

A man complete the work in 140 days

A boy can complete the work in 280 days

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