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Class 8 Exam  >  Class 8 Tests  >  Test: Linear Equations- 2 - Class 8 MCQ

Test: Linear Equations- 2 - Class 8 MCQ


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20 Questions MCQ Test - Test: Linear Equations- 2

Test: Linear Equations- 2 for Class 8 2024 is part of Class 8 preparation. The Test: Linear Equations- 2 questions and answers have been prepared according to the Class 8 exam syllabus.The Test: Linear Equations- 2 MCQs are made for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Linear Equations- 2 below.
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Test: Linear Equations- 2 - Question 1
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Solve: 4y = 20

Detailed Solution for Test: Linear Equations- 2 - Question 1
4y = 20 y = 20/4 y = 5
Test: Linear Equations- 2 - Question 2
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Solve: 3x = 2x+ 18

Detailed Solution for Test: Linear Equations- 2 - Question 2

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

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Test: Linear Equations- 2 - Question 3
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Solve: x = 4/5*(x+10)

Detailed Solution for Test: Linear Equations- 2 - Question 3

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

Test: Linear Equations- 2 - Question 4
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The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
Detailed Solution for Test: Linear Equations- 2 - Question 4

Given,

Sum of multiples of 7 = 357

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

ATP,

x + x + 7 + x + 14 = 357

3x + 21 = 357

3x = 357 - 21

3x = 336

x = 336/3

x = 112

Therefore,

the smallest multiple is x = 112 

Test: Linear Equations- 2 - Question 5
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In an equation the values of the expressions on the LHS and RHS are _______.
Test: Linear Equations- 2 - Question 6
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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.       
Detailed Solution for Test: Linear Equations- 2 - Question 6

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

Test: Linear Equations- 2 - Question 7
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Solve: x − 2 = 7
Detailed Solution for Test: Linear Equations- 2 - Question 7

X = 7 + 2

= 9

Test: Linear Equations- 2 - Question 8
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Solve: 5t – 3 = 3t – 5
Detailed Solution for Test: Linear Equations- 2 - Question 8

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

Test: Linear Equations- 2 - Question 9
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What will be the solution of these equations ax+by = a-b, bx-ay = a+b       
Detailed Solution for Test: Linear Equations- 2 - Question 9

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

Test: Linear Equations- 2 - Question 10
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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.
Detailed Solution for Test: Linear Equations- 2 - Question 10
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.
Test: Linear Equations- 2 - Question 11
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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?
Detailed Solution for Test: Linear Equations- 2 - Question 11
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
Test: Linear Equations- 2 - Question 12
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Solve: 7x = 21
Test: Linear Equations- 2 - Question 13
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Solve: 5x+ 9 = 5 + 3x
Detailed Solution for Test: Linear Equations- 2 - Question 13

5x+ 9 = 5 + 3x
5x - 3x = 5 - 9
2x = -4
x = -2

Test: Linear Equations- 2 - Question 14
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Solve: y + 3 = 10
Detailed Solution for Test: Linear Equations- 2 - Question 14

y + 3 = 10
y = 10 - 3
y = 7

Test: Linear Equations- 2 - Question 15
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Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Detailed Solution for Test: Linear Equations- 2 - Question 15

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.

Test: Linear Equations- 2 - Question 16
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The value of the expression on one side of the equality sign is _____ to the value of the expression on the other side.
Detailed Solution for Test: Linear Equations- 2 - Question 16

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

Test: Linear Equations- 2 - Question 17
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Detailed Solution for Test: Linear Equations- 2 - Question 17
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
Test: Linear Equations- 2 - Question 18
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Solve: 5a = 30
Test: Linear Equations- 2 - Question 19
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Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age. Find their present ages.
Detailed Solution for Test: Linear Equations- 2 - Question 19
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.
Test: Linear Equations- 2 - Question 20
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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.
Detailed Solution for Test: Linear Equations- 2 - Question 20

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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