Worksheet Solutions: Linear Equation | Mental Mathematics for Class 8 PDF Download

Q1: Find the value of p if, p:6p + 1/3 = 3(p-6)
Ans: P:6p+ 1/3 = 3(p-6)
P/6p+ 1/3 = 3p – 18
(1+2)/6 = 3p-18
½+18 = 3p
3p = 37/2
P = 37/6

Q2: Find the value of x, if 0.4(5x+20) = 0.8(10x-5)
Ans: 0.4(5x+20)= 0.8(10x-5)
2x+8=8x-4
-6x=-12
X= 2

Q3: The ratio of ram and rahims age is 4:5. If Ram’s age is 40,then what is Rahim’s age?
Ans: Ram:Rahim=4:5
Ram= 4x
Rahim=5x
Then, 4x=40
X=10
Therefore, Rahim’s age= 5×10=50 years

Q4: There are three consecutive three numbers whose sum is 57. Find the largest number
Ans: Let one number is x
Other two are x+2 and x+4
So,
X+(x+2)+(x+4)=57
3x+6=57
X=17
So largest number is 17+4=21

Q5: The sum of Two numbers are 67. One exceeds another by 1. Whatbis the larger number?
Ans: Let one number is x
Another number is y
So x+y=67 ———(1)
x-y=1 ———–(2)
(1)+(2) we get
2x =68
X=34

Q6: 4 years ago the sum of son and mother’s age was 44. 8 years hence their sum of age will be?
Ans: Now their sum of age is 44+8=52
8 years hence will be 52+8+8=68years

Q7: Find the value of p: 3p-77=2p+23
Ans: 3p-77=2p+23
P=100

Q8: The ratio of breadth and length of a rectangle is 3:4. If the perimeter is 84 cm. Then find the length.
Ans: Length=3x
Breadth=4x
Perimeter 2(3x+4x)=84
X=6
Therefore length is 3×6=18 m

Q9: Find the value of x: 4/x (x+8) = 48
Ans: 4/x(x+8)=48
48x=4x+32
40x=32
X= 4/5

Q10: The ratio of the ages of A and B are 5:7. The difference between their age is 20 years. What is A’s age?
Ans: A:B=5:7
A=5x
B=7x
So, 7x-5x=20
X=10
Therefore,A’s= 5×10= 50

Q11: Find the value of x, if (x-3)/(10+x) = 2/3.
Ans: (X-3)/(10+x)= 2/3
3x-9=20+2x
X= 29

Q12: The sum of four consecutive natural numbers are 38. Find the largest number.
Ans: X+(x+1)+(x+2)+(x+3)=38
4x+6=38
X=8

Q13: The ratio of number of pen and pencil is 3:4 in a box. The difference between their numbers is 10. How many pens are there?
Ans: Pen: pencil= 3:4
Pen=3x
Pencil=4x
Then,4x-3x=10
X=10
Therefore, pen=3×10=30

Q14: The ratio of the sides of a triangle is 3:4:2. If the perimeter of the triangle is 81cm. Then find the longest side.
Ans: Ratio 3:4:2
So, 3x+4x+2x= 81
9x=81
X=9
Therefore 4x= 4×9=36

Q15: The sum of three consecutive natural number is 84. Find the middle number.
Ans: X+(x+1)+(x+2)=84
X=27
So, middle number is 27+1=28

Q16: If a/b = ¾ then find the value of 3a+12b
Ans: 9+48=57

Q17: A man sells his car at 20% loss. If his cost price was 2000. What was the selling price?
Ans: Cost price =2000rs
20% of 2000= 400
Therefore selling price 2000-400= 1600 rs

Q18: Find the value of. 20% of 20% of 2000.
Ans: 20% of 2000= 2000×20/100=40
20% of 400= 400×20/100=80

Q19: Find the value of b: 5/b + 4/b = 4/5
Ans: 5/b+4/b=4/5
9/b=4/5
4b=45
B= 45/4

Q20: The length of a rectangle is twice as the breadth. The perimeter is 36 cm. Find the area.
Ans: Let Breadth=x m
So,Length= 2x m
So, 2(3x)=6xm
So, 6x=36
X=6
Therefore, length=12m
So area (6×12)m=72cm sq