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Q1. The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. The digit at the unit's place of the original number is

• 3
• 8
• 7
• 4

Solution

Let the digit at unit's place be x. Then, digit at ten's place = 11 - x According to given information, 10x + (11 - x) = 10(11 - x) + x - 45 10x + 11 - x = 110 - 10x + x - 45 9x + 11 = 65 - 9x 18x = 54 x = 3 Thus, the digit at the unit's place of the original number is 3.

Q2. If the solution of the equation 6x + 6 = 0 is -1, then the value of expression 6x + 6 is

• zero
• -1
• 1
• 5

Solution

Since x = -1 is a solution of the equation 6x + 6 = 0, we have 6x + 6 = 6(-1) + 6 = -6 + 6 = 0

Q3. 4p - 11 - p = 2 + 2p - 20.So, the value of p is 

• 0
• 7
• -7
• None of the above

Solution

4p - 11 - p = 2 + 2p - 20 ∴ 4p - p - 2p = 2 - 20 + 11 ∴ p = -7

Q4. The sum of ages of father and son is 70 years. If the son is two years less than half the age of the father, then the father's age is

• 48
• 53
• 62
• 38

Solution

Q5. Solve 3(2x - 1) + x - 9 = 11x.

• -1
• -3
• 3
• 1

Solution

3(2x - 1) + x - 9 = 11x ∴ 6x-3+x - 9=11x ∴ 7x - 11x = 12 ∴ -4x = 12 ∴ x = -3

Q6. The sum of two consecutive even numbers is 90. The smaller number is

• 34
• 44
• 20
• 14

Solution

Let the two consecutive even numbers be x + 2 and x + 4. Given, the sum of two consecutive even numbers is 90. Therefore, the required equation will be (x + 2) + (x + 4) = 90 2x + 6 = 90 2x = 84 x = 42 Thus, the smaller number = x + 2 = 42 + 2 = 44

Q7. Suzy is ten years older than Billy, and next year she will be twice as old as Billy. How old is Suzy now?

• 19 years
• 9 years
• 29 years
• 20 years

Solution

Let Billy's present age = x yearsThen, Suzy's present age = (10 + x) yearsBilly's age next year = (x + 1) yearsSuzy's age next year = (x + 10) + 1 = (x + 11) yearsAs per the given information,x + 11 = 2(x + 1)x + 11 = 2x + 22x - x = 11 - 2x = 9Hence, Billy's present age = x = 9 yearsAnd, Suzy's present age = x+  10 = 9 + 10 = 19 years

Q8. If 6x - 12 = 0, then x =

• 2
• 3
• 4
• 5

Solution

6x - 12 = 0 Transposing -12 to R.H.S., we get 6x = 12 Diving both sides by 6, we get x = 2

Q9. What is the value of x, if −1 - (2 - x) = 2 - (3x + 1)?

• -1
• 0
• 1
• None of the above

Solution

−1−2+x=2−3x−1 ∴ x + 3x = 3+ 1 ∴ 4x = 4 ∴ x = 1

Q10. The sum of the digits of a two-digit number is 10. If we interchange the digits then the new number formed is 36 less than the original. The digit at the ten's place of the original number is 

• 5
• 6
• 7
• 3

Solution

Let the two-digit number be xy = 10x + y From the given conditions, we have x + y = 10        ….(1) 10y + x = 10x + y - 36 10y - y - 10x + x = -36 9y - 9x = -36 9(y - x) = -36 y - x = -4 x - y = 4          ….(2) Adding (1) and (2), we get 2x = 14 x = 7 From (1), y = 10 - 7 = 3 Therefore, number = xy = 73 Thus, the ten's place of the original number is 7.

Q11. The value of x for the equation 3(x + 3) = 5(x - 5) also satisfies the equation

• x - 17 = 0
• x + 17 = 0
• 2x - 17 = 0
• 2x + 17 = 0

Solution

3(x + 3) = 5(x - 5) 3x + 9 = 5x - 25  3x - 5x + 9 = 5x - 25 - 5x     [Subtracting 5x from both the sides] -2x + 9 = -25 -2x = -25 - 9                        [Transposing 9 to R.H.S.] -2x = -34 x = 17                                 [Dividing throughout by 2] x - 17 = 0                            [Transposing 17 to L.H.S.]

Q12. One fifth of a number of butterflies in a garden are on jasmines and one third of them are on roses. Three times the difference of the butterflies on jasmines and roses are on lilies. If the remaining one is flying freely, the number of butterflies in the garden is

• 10
• 12
• 15
• 21

Solution

Q13. Amit is now 20 years old and Leela is 4 years old. After how many years will Amit be twice as old as Leela?

• 16 years
• 18 years
• 12 years
• 14 years

Solution

Amit's present age = 20 years Leela's present age = 4 years Let after x number of years, Amit be twice as old as Leela. After x years, Amit's age = (20 + x) years After x years, Leela's age = (4 + x) years Then, 20 + x = 2(4 + x) 20 + x = 8 + 2x 20 - 8 = 2x - x x = 12 Thus, after 12 years Amit will be twice as old as Leela.

Q14. 9 subtracted from half of a number gives 5. The number is 

• 26
• 28
• 30
• 32

Solution

Q15. Rakesh is 5 years younger than Suresh. What is the age of Suresh?

• 5 - x
• 5x
• X + 5
• None of the above

Solution

Let Rakesh’s age be x, then Suresh’s age will be x + 5.

Q16. A linear equation in one variable has

• Only one solution
• Two solutions
• More than two solutions
• No solution

Solution

A linear equation in one variable has only one solution. 

Q17. Mona's father is thrice as old as Mona. After 12 years he will be just twice his daughter. Their present ages are

• 12 years, 36 years
• 10 years, 30 years
• 12 years, 24 years
• 18 years, 36 years

Solution

Let Mona's present age = x years. Then, her father's present age = 3x years After 12 years, Mona's age = (x + 12) years Her father's age = (3x + 12) years According to the given information, 3x + 12 = 2(x + 12) 3x + 12 = 2x + 24 x = 12 then, 3x = 3(12) = 36 Thus, Mona's present age is 12 years and her father's present age is 36 years.

Q18. The biggest angle of a triangle is 10^o more then twice of the smallest angle and the third angle is 10^o more then the smallest angle. Find the smallest angle?

• 20^o
• 30^o
• 40^o
• 50^o

Solution

Let the smallest angle = s^o Then, the biggest angle = (10 + 2s)^o And, third angle = (10 + s)^o Now, sum of the angles of a triangle = 360^o Thus, we have s^o + (10 + 2s)^o + (10 + s)^o = 180^o 4s^o + 20^o = 180^o 4s^o = 160^o s^o = 40^o Thus, the smallest angle of a triangle is 40^o.

Q19. The linear equation to represent perimeter p of a rectangle whose side is l and breadth is b will be given by

• p = l + b
• p = (l + 2b)
• p = (2l + b)
• p = 2(l + b)

Solution

Q20. Sum of two numbers is 74. If one exceeds the other by 10, find the numbers?

• 32, 42
• 60, 14
• 52, 22
• 50, 24

Solution

Let the one number be x. Then, another number will be x + 10. According to the question, x + (x + 10) = 74 2x + 10 =7 4 2x = 74 - 10 2x = 64 x = 32 Therefore, one number is 32. And, the other number is x + 10 = 32 + 10 = 42.

Q21. Ali's father is 45 years old. He is 15 years older than twice Ali's age. How old is Ali?

• 12 years
• 15 years
• 17 years
• 16 years

Solution

Let Ali's age = xThen, his father's age = 2x + 15According to the question, father's age = 45 Thus, 2x + 15 = 452x = 45 - 15 2x = 30 x = 15Therefore, Ali is 15 years old.

Q22. Solve 3x + (-1 + 2) = x + 3? 

• -1
• 1
• -2
• 2

Solution

3x +1 = x +3 ∴2x=2 ∴x=1 

Q23. The ages of Ashu and Raju are in the ratio 5: 7. If Ashu was 9 years older and Raju 9 years younger, the age of Ashu would have been twice the age of Raju. Find their present ages.

• 3 years and 21 years
• 15 years and 21 years
• 15 years and 24 years
• 24 years and 30 years

Solution

Given, the ages of Ashu and Raju are in the ratio 5: 7. Let the age of Ashu be 5x and age of Raju be 7x. If Ashu was 9 years older, then his age would be (5x + 9) years If Raju was 9 years younger, then his age would be (7x - 9) years From the given information, 5x + 9 = 2(7x - 9) 5x + 9 = 14x - 18 14x - 5x = 9 + 18 9x = 27 x = 3 Thus, Ashu's present age is 15 years and Raju's present age is 21 years.

Q24. When 10 is added to six times a number, the result is 22. Find the number.

• 1
• 2
• 3
• 4

Solution

Let the number be x. ∴10+6x=22 ∴ 6x= 12 ∴ x = 2 

Q25. 45 added to a number gives 90. The number is 

• 45
• 64
• 35
• 55

Solution

Let the required number be x. Then, x + 45 = 90 x = 90 - 45 = 45

Q26. For what value of x, the equation 2x + 4 = x + 8 is satisfied?

• 10
• -12
• 20
• 4

Solution

2x + 4 = x + 8 2x - x = 8 - 4    [By transposition] x = 4

Q27. The linear equation 2x + 6 = ______ can represent the price of two products which differ by Rs. 6 and their prices add up to give 45.

• 45
• 40
• 35
• zero

Solution

Since, the prices of two products differ by Rs. 6, their prices will be x and x + 6. Sum of prices = 45 (Given) So, required equation is x + x + 6 = 45 2x + 6 = 45

Q28. The sum of two consecutive even numbers is 90. The linear equation representing this condition is

• x + 6 = 90
• 2x + 6 = 90
• x + 2 = 90
• 2x + 2 = 90

Solution

Let the two consecutive even numbers be (x + 2) and (x + 4). Given, the sum of two consecutive even numbers is 90. Therefore, the required equation will be (x + 2) + (x + 4) = 90 2x + 6 = 90

Q29. What is the linear equation obtained by adding 7 to both sides of the equation 3x - 7 = 5x + 2 and then transposing 5x to left hand side of the equation?

• -2x = 9
•  2x = 9   
• -7 + 2 = 5x - 3x
• -7 - 2 = 5x + 3x

Solution

3x - 7 = 5x + 2 is the given equation. Adding 7 to both sides, 3x - 7 + 7 = 5x + 2 + 7 3x = 5x + 9 Transposing 5x to left hand side, 3x - 5x = 9 -2x = 9

Q30. The sum of the digits of a two-digit number is 12. The unit's digit is three times the ten's digit. Find the number.

• 39
• 93
• 26
• 62

Solution

Let the digit at the unit's place = x Then the digit at the ten's place = 12 - x According to given information, we have x = 3(12 - x) x = 36 - 3x 4x = 36 x = 9 Thus, the digit at the ten's place = 12 - x = 12 - 9 = 3 Hence, the number is 39.

Q31. The two numbers are such that one number exceeds the other by 9 and their sum is 29. The smaller number is 

• 18
• 10
• 7
• 6

Solution

Let the smaller number  = x Then, the larger number  = x + 9 Given, sum of the two numbers = 29 So, x + (x + 9) = 29 2x + 9 = 29 2x = 20 x = 10 Thus, the smaller number is 10.

Q32. The linear equation 2x + 5 = __________ can represent the age of two siblings which differ by 5 years and their ages add up to give 25.

• 25
• 38
• 15
• zero

Solution

Since, the ages of the two siblings differ by 5 years, their ages will be x and x + 5. Sum of ages = 25 (Given) So, required equation is x + x + 5 = 25 or 2x + 5 = 25

Q33. If 0.06(x - 5) = 0.04(x + 8), then x =

• 31
• 20
• 15
• 11

Solution

Q34. The value of x which satisfies the linear equation 0.25(x + 18) = 0.50(3 - x) is 

• -3
• -4
• -5
• -2

Solution

Q35. The sum of two numbers is 80 and their ratio is 3 : 5. The greatest amongst the two numbers is

• 20
• 30
• 40
• 50

Solution

Q36. One-fourth of a number decreased by 4 is equal to 11. What is the number?

• 40
• 44
• 60
• 64

Solution

Q37. The sum of two consecutive natural numbers is 45.Find the numbers. (Use y to represent ‘the numbers’.)

• 19,20
• 21,22
• 23,22
• None of the above

Solution

The consecutive natural numbers are y and y + 1. ∴ y+y+1=45  ∴ 2y=44 ∴ y = 22 and y+1 =23

Q38. The sum of two consecutive multiples of 13 is 117. One of these multiples is

• 39
• 52
• 78
• 91

Solution

Q39. The area of a rectangle is 24 cm². If its width is 6 cm, then length is

• 4 cm
• 8 cm
• 12 cm
• 1 cm

Solution

Q40. Three consecutive integers add up to give 30. If first integer is x, linear equation representing this is 

• 3x = 27
• 3x = 30
• 3x + 3 = 27
• 3x - 3 = 30

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