CBSE Class 8 Maths Linear Equations in One Variable Worksheet

Question. Find the value of x if x/5 + x/3 + 7 = x
Answer : 15

Question. If x = 2p – 1 and y = p + 7 and x + y = 6 then find p.
Answer : p = 0

Question. Solve for x : 9x + 36 = 4x + 91
Answer : 11

Question. Find x if 3/x + 6 = 1
Answer : x = - (3/4)

Question. Simplify : (x + 7)² – (x – 7)²
Answer : 28x

Question. Find k if 13/39 = k / k + 4
Answer : k = 2

Question. Sides of a rectangle are in the ratio 14:3. If the perimeter of the rectangle is 170 cms, find the length and breadth.
Answer : 70 cm, 15 cm

Question. The perimeter of the square is 44 cm. Find its side.
Answer : 11 cm

Question. Find three consecutive odd numbers whose sum is 147.
Answer : 47, 49, 51.

Question. If one is subtracted from the number if becomes 4/5 Find the initial number
Answer : 9/5

Question. If m = x – 2 then find x in the equation 3x + 2m = 6.
Answer : x = 2

Question. Solve for x, -2 + x / 3 + x = 6
Answer : –4

Question. If x = k then find the value of k if (x + 1) + k – 2 = 0.
Answer : k = 1/2

Question. Two numbers are in the ratio 4:7. If the sum of numbers is 143, find the numbers.
Answer : 70 cm, 15 cm

Question. A mother is four times as old as her daughter. If the difference of their ages is 36 years. Find the age of daughter.
Answer : 12 years

Question. If father is twice as old as his son and also 29 years older than his son. What is the age of father?
Answer : 58 years.

Question. A person starts his job with a monthly salary of Rs. 5000 and earn a fixed increment after every year. If he gets Rs. 6000 after 5 years. Find his annual increment,
Answer :   Rs. 250

Please click on below link to download CBSE Class 8 Maths Linear Equations in One Variable Worksheet

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EXERCISE - I (FOUNDATION CORNER)

Question. 1. The difference between a number and its three-fifth is 50. What is the number ?
(a) 75
(b) 100
(c) 125
(d) None of these
Answer: C

Question. 2. If a number is decreased by 4 and divided by 6, the result is 8. What would be the result if 2 is subtracted from the number and then it is divided by 5?
(a) \( 9\frac{2}{3} \)
(b) 10
(c) \( 11\frac{1}{5} \)
(d) None of these
Answer: B

Question. 3. If one-third of one-fourth of a number is 15, then three-tenth of that number is :
(a) 35
(b) 36
(c) 45
(d) 54
Answer: D

Question. 4. A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?
(a) 3.5
(b) 6
(c) 8
(d) None of these
Answer: C

Question. 5. Three-fourth of a number is 60 more than its one-third. The number is :
(a) 84
(b) 108
(c) 144
(d) None of these
Answer: C

Question. 6. When 24 is subtracted from a number, it reduces to its four-seventh. What is the sum of the digits of that number?
(a) 1
(b) 9
(c) 11
(d) None of these
Answer: C

Question. 7. Find the number which when multiplied by 15 is increased by 196.
(a) 14
(b) 20
(c) 26
(d) 28
Answer: A

Question. 8. If a number, when divided by 4, is reduced by 21, the number is :
(a) 18
(b) 20
(c) 28
(d) 38
Answer: C

Question. 9. A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is
(a) 240
(b) 260
(c) 270
(d) 280
Answer: D

Question. 10. The difference of two numbers is \( 20\% \) of the larger number. If the smaller number is 12, the larger one is :
(a) 15
(b) 16
(c) 18
(d) 20
Answer: A

Question. 11. If one-seventh of a number exceeds its eleventh part by 100, then the number is :
(a) 770
(b) 1100
(c) 1825
(d) 1925
Answer: D

Question. 12. If the sum of one-half and one-fifth of a number exceeds one-third of that number by \( 7\frac{1}{3} \), the number is
(a) 15
(b) 18
(c) 20
(d) 30
Answer: C

Question. 13. If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is:
(a) 2
(b) 3
(c) 4
(d) 6
Answer: C

Question. 14. If 50 is subtracted from two-third of a number, the result is equal to sum of 40 and one fourth of that number. What is the number ?
(a) 174
(b) 216
(c) 246
(d) 336
Answer: B

Question. 15. If the sum of a number and its square is 182, what is the number ?
(a) 15
(b) 26
(c) 28
(d) None of these
Answer: D

Question. 16. Twenty times a positive integer is less than its square by 96. What is the integer ?
(a) 20
(b) 24
(c) Cannot be determined
(d) None of these
Answer: B

Question. 17. Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is :
(a) 4
(b) 5
(c) 6
(d) 10
Answer: B

Question. 18. The sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root ?
(a) 8
(b) 27
(c) 32
(d) None of these
Answer: A

Question. 19. Two-third of a positive number and \( \frac{216}{25} \) of its reciprocal are equal. The number is :
(a) \( \frac{12}{5} \)
(b) \( \frac{5}{12} \)
(c) \( \frac{144}{25} \)
(d) \( \frac{25}{144} \)
Answer: A

Question. 20. Find a positive number when increased by 17 is equal to 60 times the reciprocal of the number.
(a) 3
(b) 10
(c) 17
(d) 20
Answer: A

EXERCISE - II (COMPETITIVE CORNER)

Question. 1. A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is:
(a) 3
(b) 5
(c) 7
(d) 9
Answer: C

Question. 2. The sum of a positve number and its reciprocal is thrice the difference of the number and its reciprocal. The number is:
(a) \( \sqrt{2} \)
(b) \( \frac{1}{\sqrt{2}} \)
(c) \( \sqrt{3} \)
(d) \( \frac{1}{\sqrt{3}} \)
Answer: A

Question. 3. The product of two natural numbers is 17. Then, the sum of the reciprocals of their square is :
(a) \( \frac{1}{289} \)
(b) \( \frac{289}{290} \)
(c) \( \frac{290}{289} \)
(d) 289
Answer: C

Question. 4. If \( 2\frac{1}{2} \) is added to a number and the sum multiplied by \( 4\frac{1}{2} \) and 3 is added to the product and then dividing the sum by \( 1\frac{1}{5} \), the quotient become 25. What is the number?
(a) \( 2\frac{1}{2} \)
(b) \( 3\frac{1}{2} \)
(c) \( 4\frac{1}{2} \)
(d) \( 5\frac{1}{2} \)
Answer: B

Question. 5. Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :
(a) 30
(b) 32
(c) 36
(d) 42
Answer: A

Question. 6. Three numbers are in the ratio 3 : 4 : 6 and their product is 1944. The largest of these number is :
(a) 6
(b) 12
(c) 18
(d) None of these
Answer: C

Question. 7. Two numbers are such that the square of one is 244 less than 8 times the square of the other. If the number be in ratio 3 : 4 the number are:
(a) 6, 8
(b) 9, 12
(c) 12, 16
(d) None of these
Answer: A

Question. 8. Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is :
(a) 36
(b) 48
(c) 56
(d) 64
Answer: C

Question. 9. The sum of three numbers is 264. If the first number be twice the second and third number be one-third of the first, then the second number is :
(a) 48
(b) 54
(c) 72
(d) 84
Answer: C

Question. 10. The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is :
(a) 10
(b) 12
(c) 15
(d) 16
Answer: B

Question. 11. One-fifth of a number is equal to \( \frac{5}{8} \) of another number. If 35 is added to the first number, it becomes four times of the second number. The second number is:
(a) 25
(b) 40
(c) 70
(d) 125
Answer: B

Question. 12. The sum of two numbers is 25 and their difference is 13, Find their product :
(a) 104
(b) 114
(c) 315
(d) 325
Answer: B

Question. 13. If the sum of two numbers is 33 and their difference is 15, the smaller number is :
(a) 9
(b) 12
(c) 15
(d) 18
Answer: A

Question. 14. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :
(a) 11 : 9
(b) 11 : 18
(c) 21 : 19
(d) 22 : 9
Answer: A

Question. 15. The product of two number is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers ?
(a) 12
(b) 14
(c) 16
(d) 18
Answer: A

Question. 16. Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin ?
(a) 16 years
(b) 18 years
(c) 28 years
(d) None of these
Answer: D

Question. 17. The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(a) 3 : 4
(b) 3 : 5
(c) 4 : 3
(d) None of these
Answer: D

Question. 18. The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q’s present age and P’s age after 6 years is 2, what is the total of P’s and Q’s present ages ?
(a) 48 years
(b) 52 years
(c) 56 years
(d) None of these
Answer: A

Question. 19. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present?
(a) 12 years
(b) 15 years
(c) \( 19\frac{1}{2} \) years
(d) 21 years
Answer: B

Question. 20. Present ages of X and Y are in the ratio 5 : 6 respectively. Seven years hence this ratio will be become 6 : 7 respectively. What is X’s present age in years ?
(a) 35
(b) 42
(c) 49
(d) Cannot be determined
Answer: A

Question. 21. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?
(a) 24
(b) 27
(c) 40
(d) Cannot be determined
Answer: A

Question. 22. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present ?
(a) 16 years
(b) 18 years
(c) 20 years
(d) Cannot be determined
Answer: A

Question. 23. The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Saransh?
(a) 24 years
(b) 32 years
(c) 34 years
(d) 38 years
Answer: D

Question. 24. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years ?
(a) 1 : 4
(b) 2 : 3
(c) 3 : 5
(d) 5 : 6
Answer: C

Question. 25. Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5 ?
(a) 5 years
(b) 10 years
(c) 20 years
(d) 37 years
Answer: B

Question. 26. The ratio of the father’s age to his son’s age is 7 : 3. The product of their ages is 756. The ratio of their ages after 6 years will be :
(a) 5 : 2
(b) 2 : 1
(c) 11 : 7
(d) 13 : 9
Answer: B

Question. 27. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(a) 8, 20, 28
(b) 16, 28, 36
(c) 20, 35, 45
(d) None of these
Answer: B

Question. 28. The ratio of the ages of a man and his wife is 4 : 3. After 4 years, this ratio will be 9 : 7. If at the time of marriage, the ratio was 5 : 3, then how many years ago were they married ?
(a) 8 years
(b) 10 years
(c) 12 years
(d) 15 years
Answer: B

Question. 29. The ratio between the school ages of Neelam and Shaan is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shaan’s age is 5 : 9, then what is the school age of Shaan?
(a) 25 years
(b) 30 years
(c) 36 years
(d) Cannot be determined
Answer: C

Question. 30. The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A’s age 4 years ago and B’s age 4 years hence 1 : 1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?
(a) 1 : 3
(b) 2 : 1
(c) 3 : 1
(d) 4 : 1
Answer: C

Question. 31. Ten years ago, A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages ?
(a) 20 years
(b) 30 years
(c) 45 years
(d) None of these
Answer: D

Question. 32. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B ?
(a) 7
(b) 8
(c) 9
(d) 10
Answer: D

Question. 33. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:
(a) 14
(b) 18 years
(c) 20 years
(d) 22 years
Answer: D

Question. 34. Eighteen years ago, a father was three times as old as his son. Then the sum of the present ages of the son and the father is:
(a) 54
(b) 72
(c) 105
(d) 108
Answer: D

Question. 35. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. How old is the mother at present?
(a) 32 years
(b) 36 years
(c) 40 years
(d) 48 years
Answer: C

Question. 36. Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Tanya’s age to that of her grandfather?
(a) 1 : 2
(b) 1 : 5
(c) 3 : 8
(d) None of these
Answer: D

Question. 37. The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is :
(a) 5 : 2
(b) 7 : 3
(c) 9 : 2
(d) 13 : 4
Answer: B

Question. 38. Four years ago, the father’s age was three times the age of his son. The total of the ages of the father and the son after four years, will be 64 years. What is the father’s age at present?
(a) 32 years
(b) 36 years
(c) 44 years
(d) None of these
Answer: D

Question. 39. One year ago, Promila was four times as old as her daughter Sakshi. Six years hence, Promila age will exceed her daughter age by 9 year the ratio of the present ages of Promila and her daugther is:
(a) 9 : 2
(b) 11 : 3
(c) 12 : 5
(d) 13 : 4
Answer: D

Question. 40. The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be:
(a) 12 years
(b) 14 years
(c) 18 years
(d) 20 years
Answer: D