Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 2 Linear Equations in One Variable Questions Solution. In this chapter, there is total 40 math problems. We have given each questions solution step by step.
1.) Find the value of : + = ( − ) +
ANSWER:
+ = ( − ) +
+ = − +
+ = + 6
By rearranging terms,
3x – x = 6 – 4
2x = 2
X = 2/2
X = 1
2.) Find the value of :
/( + ) =
ANSWER:
/( + ) =
/7 + 4 =
/7= 4 – 4
/7 = 0
Y = 0
3.) Find the value of :
−/ (−) = /
ANSWER:
−/ (−) = /
By using cross multiplication,
8 x (−) = 5 x (−)
56 -8z = 70 – 15z
By rearranging,
56 – 70 = -15z + 8z
-14 = -7z
Z = 2
4.) Find the value of :
/ – / = /
ANSWER:
/ – / = /
We make denominator same by LCM.
We make denominator 12.
4a/ 12 – 3a / 12 = /
a / 12 = /
By comparing,
a = 7
5.) Find the value of :
/ + / = /
ANSWER:
/ + / = /
We make denominator same by LCM.
We make denominator 6.
3b/6 +2b/6 = 1/6
5b/6 = 1/6
By comparing,
5b = 1
b = 1/5
6.) Find the value of : 2( − ) = ( + )
ANSWER:
2( − ) = ( + )
2 − 6 = 10c + 10
By rearranging terms,
2– 10c = 10 + 6
-8c = 16
C = 16 / -8
C = -2
7.) Solve: 0.16( + ) = . + .
ANSWER:
0.16( + ) = . + .
0.8x + 0.16 = . + .
By rearranging terms,
0.8x -. = . – 0.16
. = 0
X = 0
8.) Solve for : − ( + )( − ) =
ANSWER:
− ( + )( − ) =
– x ( − ) – 1( − ) = 0
–+x – x + 2 = 0
x + 2 = 0
x = -2
9.) What is the number which when added to 15 times of itself gives 208.
ANSWER:
Let, the number is x.
x + 15x = 208
16x = 208
X = 208 / 16
X = 13
10.) A number is as much greater than 84 as it is less than 108. What is the number?
ANSWER:
Let, the number is x.
We form equation.
84 + x = 108 – x
By rearranging,
x + x = 108 – 84
2x = 24
X = 12
Now the number is 84 + 12 = 108 – 12 = 96.
11.) The sum of three consecutive natural numbers is 33. Find the numbers.
ANSWER:
Given that,
The sum of three consecutive natural numbers is 33.
Let, 1st natural number is x. then consecutive natural number is x + 1 and x + 2.
X + x+ 1 + x + 2 = 33
3x + 3 = 33
3x = 33 – 3
3x = 30
X = 30 / 3
X = 10.
Three consecutive natural numbers 10, 11 and 12.
12.) Two consecutive sides of a rectangle are in the ratio 3:2. If its perimeter is 150cm, then find its area?
ANSWER:
Given that,
Two consecutive sides of a rectangle are in the ratio 3:2.
Perimeter of rectangle is 150cm.
We know,
Perimeter of rectangle = 2 x (Length + breadth)
Let, Length and breadth of rectangle is 3x and 2x respectively.
Perimeter of rectangle = 2 x (3x+2x)
Perimeter of rectangle = 10x = 150cm.
x = 150cm. /10
x = 15 cm.
But, Length of rectangle is 3x = 3 x 15 = 45 cm
Breadth of rectangle = 2x = 2 x 15 = 30 cm.
Now area of rectangle = (Length x breadth)
Area of rectangle = 45 x 30 = 1350 cm2
13.) A number consists of two digits whose sum is 9. If 27 is added to the number its digits are reversed. Find the number.
ANSWER:
Given that,
A number consists of two digits whose sum is 9.
27 is added to the number its digits are reversed.
X + y = 9
By trial and error method,
If we put x = 3 and y = 6
3 + 6 = 9
Now if we add 27 in 36 we get,
36 + 27 = 63 which is reverse.
The number is 36.
14.) A man sold an umbrella for Rs.495 and gained 10% on it. Find its cost price.
ANSWER:
Given that,
A man sold an umbrella for Rs.495
Selling Price =Rs.495
Gained 10% on it.
We have to find cost price.
We know cost price is 100% price.
We gain 10% profit.
Selling price= 100 + 10 = 110%
Now,
110% = Rs.495
100% = ?
By cross Multiplication,
Rs.495 x 100
———————
110
Cost price ofan umbrella = Rs. 450
15.) /th of a number is 20 more than half of the same number. What is the number?
ANSWER:
Given that,
/th of a number is 20 more than half of the same number.
Let, the number is x.
We form equation.
3x/4 = x/2 + 20
3x/4 – x/2 = 20
We make denominator same.
3x – 2x / 4 = 20
X = 20 x 4
X = 80
The number is 80.
16.) Three fourth of a number exceeds its one third by 60. What is the number?
ANSWER:
Given that,
Three fourth of a number exceeds its one third by 60.
Let, the number is x.
3x/4 – x / 3 = 60
We make denominator same.
9x – 4x / 12 = 60
5x = 60 x 12
X = 12 x 12
X = 144
The number is 144.
17.) Sum of three consecutive multiples of 4 is 108. Find the numbers.
ANSWER:
Given that,
Sum of three consecutive multiples of 4 is 108.
Let, First multiple of 4 is 4x.
2nd consecutive multiple of 4 is 4x + 4
3rd consecutive multipleof 4 is 4x + 8
We form equation.
4x +4x + 4 +4x + 8 = 108
12x + 12 = 108
12 x = 96
X = 96 / 12
X = 8
First multiple of 4 is 4x. = 4 x 8 = 32
2nd consecutive multiple of 4 is 4x + 4 = 32 + 4 = 36
3rd consecutive multiple of 4 is 4x + 8 = 32 + 8 = 40
18.) A box of toffees is divided among 24 children. They will get 5 toffees each. How many would each get, if the number of children is reduced by 4?
ANSWER:
Given,
A box of toffees is divided among 24 children
They will get 5 toffees each.
We have to find, how many would each get, if the number of children is reduced by 4.
Total number of toffees = 24 x 5 = 120 toffees
Now, ifthe number of children is reduced by 4= 24 – 4 = 20
Each would get = 120 / 20
Each would get = 6 toffees.
19.) Four fifth of a certain number is 64. What will be half of that number?
ANSWER:
Given that,
Four fifth of a certain number is 64.
We have to find half of that number.
Let, the number is x.
4x / 5 = 64
4x = 64 x 5
4x = 320
X = 320 / 4
X = 80
The number is 80.
Now, half of the number = 80 / 2 = 40
20.) Sides of a triangle are in the ratio 2:3:4. If its perimeter is 225m, find the length of smallest side.
ANSWER:
Given that,
Sides of a triangle are in the ratio 2:3:4.
Perimeter of a triangle is 225m.
Let, Sides of a triangle are 2x, 3x and 4x.
2x + 3x + 4x = 225 m
9x = 225
x = 225 / 9
x = 25
Now,
Sides of a triangle are 2x, 3x and 4x.
2 x 25, 3 x 25 and 4 x 25
Sides of a triangle are 50 m, 75m and 100m.
21.) Find the number whose fifth part increased by 5 is equal to its fourth part decreased by 5.
ANSWER:
Let,the number is x.
We form equation.
X /5 + 5 = x / 4 – 5
By rearranging,
X / 5 – x / 4 = -5 -5
4x – 5x / 20 = -10
-x = -200
X = 200
The number is 200.
22.) Find three consecutive odd natural numbers whose sum is 147.
ANSWER:
Let, the 1st natural number is x.
Consecutive odd natural numbers are x + 2 and x + 4
X +x + 2 + x + 4 = 147
3x + 6 = 147
3x = 147 – 6
3x = 141
X = 141 / 3
X = 47
1st natural number is 47.
Consecutive odd natural numbers are 49 and 51.
23.) Find three consecutive even natural numbers whose sum is 234.
ANSWER:
Let, the 1st natural number is x.
Consecutive even natural numbers are x + 2 and x + 4
X +x + 2 + x + 4 = 234
3x + 6 = 234
3x = 234 – 6
3x = 228
X = 228 / 3
X = 76
1st natural number is 76.
Consecutive even natural numbers are 78 and 80.
24.) The sum of two numbers is 95. If one number exceeds the other by 15, find the smaller number.
ANSWER:
Let, two numbers are x and y.
X + Y = 95
X – Y = 15
On solving,
2x = 110
X = 55
We put X = 55 inX + Y = 95
55 + Y = 95
Y = 95 – 55
Y = 40
The smaller number is 40.
25.) The sum of three consecutive natural numbers is 108. Find the middle number.
ANSWER:
The sum of three consecutive natural numbers is 108.
Let, 1st natural number is x. then consecutive natural number is x + 1 and x + 2.
X + x+ 1 + x + 2 = 108
3x + 3 = 108
3x = 108 – 3
3x = 105
X = 105 / 3
X = 35.
The middle numberx + 1 = 35 + 1 = 36
26.) The base of an isosceles triangle is 8 cm and its perimeter is 20 cm. Find the length of equal sides.
ANSWER:
Given that,
The base of an isosceles triangle is 8 cm.
Perimeter is 20 cm.
We know two sides of an isosceles triangle are equal.
Let, Equal side length is x.
X + x + 8 = 20 cm.
2x = 20 – 8
2x = 12
X = 6 cm.
The length of equal sidesof an isosceles triangle is 6 cm.
27.) Four fifth of a number is greater than three fourth of the same number by 4. Find the number.
ANSWER:
Let, the number is x.
4x/5 – 3x/4 = 4
We make denominator same.
16x -15x / 20 = 4
X = 80
The number is 80.
28.) The width of a rectangle is two third of its length. If the perimeter is 180m, find its dimensions.
ANSWER:
Given that,
The width of a rectangle is two third of its length.
The perimeter is 180m
We have to find its dimensions.
Let, Length of rectangle is x.
Width of rectangle is two third of its length. = 2x / 3
We know,
Perimeter of rectangle = 2 x (Length + width)
Perimeter of rectangle = 2 x (x + 2x/3)
Perimeter of rectangle = 2 x (5x / 3)
10x / 3 = 180
10 x = 540
X = 54 m.
But x is Length of rectangle.
Length of rectangle = 54 m.
Width of rectangle is two third of its length. = 2x 54 / 3
Width of rectangle = 36 m.
29.) If 10 is added to four times a certain number, the result is 5 less than five times the number. Find the number.
ANSWER:
Let, the number is x.
4x + 10 = 5x – 5
On rearranging,
10 + 5 = 5x – 4x
15 = x
The number is 15.
30.) The average age of 3 girls is 20 years and their ages are in the ratio 3:5.7. Find the age of the eldest girl.
ANSWER:
Given that,
. The average age of 3 girls is 20 years.
Ages are in the ratio 3:5.7.
Let, ages of girls are 3x, 5x and 7x respectively.
Sum of ages of girls = 3 x the average age of 3 girls
Sum of ages of girls = 3 x 20 = 60 year.
3x + 5x + 7x = 60
15 x = 60
X = 4
Ages of 3 girls are 3x = 3 x 4 = 12 years.
5x = 5 x 4 = 20 year.
7x = 7 x 4 = 28 year
31.) The perimeter of a rectangle is numerically equal to the area of the rectangle. If the width of the rectangle is 3cm, find its length.
ANSWER:
We know,
The perimeter of a rectangle = 2 x (Length + breadth)
Area of the rectangle = (Length x breadth)
The width of the rectangle is 3cm
Now,
Let length is x.
2 x (x + 3) = 3x
2x + 6 = 3x
X = 6
X is Length of Rectangle.
Length of Rectangle is 6cm.
32.) An angle is double of its supplementary angle. Find the complementary angle of its supplementary angle.
ANSWER:
Given that,
An angle is double of its supplementary angle.
We have to find,
The complementary angle of its supplementary angle.
We know,
Angle + supplementary angle = 1800
X + 2x = 1800
3x = 1800
x = 600
Now,
The complementary angle + supplementary angle =900
The complementary angle = 900– 600
The complementary angle = 300
33.) The number of boys and girls in a class are in the ratio 4:7. If the number of boys are 6 less than the number of girls. Find the number of students in the class.
ANSWER:
Given that,
The number of boys and girls in a class are in the ratio 4:7.
The number of boys and girls in a class are 4x and 7x respectively.
The number of boys are 6 less than the number of girls.
7x – 4x = 6
3x = 6
X = 2
The number of boys and girls in a class are 4x and 7x
The number of boys = 4 x 2 = 8
The number ofgirls = 7 x 2 = 14
34.) After 4 years ‘A’ will be 3 times as old as he was 4 years ago. Find his present age.
ANSWER:
Let, age of A is x.
We form equation.
X + 4 = 3 x (x – 4)
X + 4 = 3x – 12
By rearranging,
12 + 4 = 3x – x
2x = 16
X = 8
Present age of A is 8 year.
35.) In an examination a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts 75 questions and scores 125 marks, then find the number of correct questions he answered.
ANSWER:
Given that,
In an examination a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer.
He attempts 75 questions and scores 125 marks.
We have to find the number of correct questions he answered.
He attempts 75 questions = 75 x 4 = 300 marks.
If all 75 questions correct he will get 300 marks.
By trial and error method,
If 40 questions are correct.
40 x 4 =160 marks.
Number of incorrect questions = 75 – 40 = 35
We have to minus 35 marks.
160 – 35 = 125 marks.
Number of correct questions are 40.
36.) ‘A’ is 20 years older than B, he is also 6 times as old as B. What are their ages?
ANSWER:
A – B = 20 years and,
A = 6B
We put,A = 6B
6B – B = 20 years
5B = 20 years
B = 4 years.
A = 6B
A = 6 x 4 years.
A = 24 Years.
37.) One third of a number is 10 less than two third of the number. Find the number.
ANSWER:
Given that,
One third of a number is 10 less than two third of the number.
Let, the number is x.
We form equation,
2x / 3 – x / 3 = 10
X / 3 = 10
X = 30
The number is 30.
38.) One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 2:3, find the angles of the triangles.
ANSWER:
The ratio of the other two angles is 2:3
The two angles of triangle are 2x and 3x.
One of the angles of a triangle is equal to the sum of the other two angles
3rd angle = 2x + 3x = 5x
We know, sum of angles of triangle = 1800
2x + 3x + 5x = 1800
10 x =1800
x = 180
The two angles of triangle are 2x and 3x.
2x = 2 x 18 = 360
3x = 3 x 18 = 540
5x = 5 x 18 = 900
39.) Find three consecutive even natural numbers whose sum is 216.
ANSWER:
Let, the 1st natural number is x.
Consecutive even natural numbers are x + 2 and x + 4
X +x + 2 + x + 4 = 216
3x + 6 = 216
3x = 216 – 6
3x = 210
X = 210 / 3
X = 70
1st natural number is 70.
Consecutive even natural numbers are 72 and 74.
40.) Find a number whose double is 45 greater than its half.
ANSWER:
Let,the number is x.
We form equation.
2x = x/2 + 45
2x = x + 90 / 2
4x = x + 90
4x – x = 90
3x = 90
X = 90 / 3
X = 30
The number is 30.
Also See: Mental Maths Class 8 Rational Numbers Question Answer