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Q1. Sum of 3 and twice of a number is 15. The linear equation for the statement is

• 3x + 2 = 15
• 2x + 3 = 10
• 2x + 15 = 3
• 2x + 3 = 15

Solution

Let the number be xHence, twice a number = 2x Thus, the linear equation will be 3 + 2x = 15

Q2. For x = 5, we can construct which of the following equation?

• 3x - 15 = 0
• 3x + 1 = 7
• 3x - 5 = -10
• 3x + 5 = 25

Solution

That means x = 5 is satisfying the equation 3x - 15 = 0. Hence, option (A)

Q3. A two digit number like the number 63 can be expressed as 6(10) + 3(1) as 6 is a digit at the ten's place and 3 is a digit at the unit's place. Now the sum of the digits of a two digit number is 6. On adding 18 to the number, Its digits are interchanged. Then the number is :

• 23
• 24
• 26
• 25

Solution

Q4. Thrice a number when increased by 6 gives 24. The number is

• 6
• 7
• 8
• 11

Solution

Q5. Divide 64 into two parts such that one part is 38 more than the other. The other part is

• 17
• 13
• 15
• 14

Solution

Q6. Solution of 2x - 1 = 1 is

• 1
• -1
• 2
• 0

Solution

2x - 1 = 1Transposing -1 to RHS, we get2x = 2x = 1

Q7. The solution of equation 3 (x + 1) - 2(x + 1) = 5 is

• x = 4
• x = 5
• x = 0
• x = 3

Solution

Q8. The solution of the equation 3x + 4 = 25 is

• 7
• 8
• 9
• 6

Solution

3x + 4 = 25Transposing 4 to R.H.S, we get3x = 25  -  43x = 21Dividing both sides by 3, we getx = 7

Q9. Solution of equation 2x + 3 = 17 is:

• 7
• 5
• 6
• 4

Solution

2x + 3 = 17 Transposing 3 to RHS, 2x = 17 - 3 2x = 14 Dividing both the sides by 2, we get x = 7

Q10. The linear equation for the statement "Twice a number subtracted from 29 gives 11" is

• 2x - 11 = 29
• 2x - 29 = 11
• 29 - 2x = 11
• 11 - 2x = 29

Solution

Let the number be xTwice a number subtracted from 29 is 29 - 2xTwice a number subtracted from 29 gives 11 is written in linear form as 29 - 2x = 11

Q11. Which of the following will not maintain the balance of equation?

• Adding 5 on both sides
• Subtracting 10 from both sides
• Multiplying 4 on both sides
• Adding 5 on left side and adding 2 on right side

Solution

Adding 5 on left side and adding 2 on right side. We should add the same number to both the sides.

Q12. The solution of equation 5(x - 1) = 30 is:

• 6
• 7
• 5
• 4

Solution

5(x - 1) = 30 5x - 5 = 30 Transposing -5 to RHS, 5x = 30 + 5 5x = 35 Dividing both the sides by 5, X = 7

Q13. Thrice a number added to 3 gives 7 can be expressed as:

• 7 + 3x = 3
• 3x + 3 = 7
• 3x - 7 = 3
• 3x - 3 = 7

Solution

Let the number be xThrice x = 3x3 added to thrice x gives 7 means3x + 3 = 7

Q14. The sum of two angles is 90^o and the difference between them is 10^o. Then the smaller angle is

• 60^o
• 40^o
• 54^o
• 64^o

Solution

Let the smaller angle be x Then the other angle will be 90⁰ - x Difference between two angles is 100. Thus, 90⁰ - x - x = 10⁰ i.e. 2x = 90⁰ - 10⁰ i.e. 2x = 80⁰ i.e. x = 40⁰

Q15. 4 times a number added to 5 gives 7 can be represented by which of the following linear equation?

• 4x + 7 = 5
• 4x - 7 = 5
• 4x - 5 = 7
• 4x +5 = 7

Solution

Let the number be x4 times a number added to 5 gives 4x + 54 times a number added to 5 gives 7 means 4x + 5 = 7

Q16. Karim's father is 8 times as old as Karim. If his father is 48 years, then the age of Karim is

• 7 years
• 6 years
• 9 years
• 12 years

Solution

Let the age of Karim be xAge of Karim's father = 8x8x = 48x = 6Karim's age = 6 years

Q17. 6 times Rohit's age is 28 less than twice the age of his father. If his father is 32 years old, then Rohit's age is

• 6 Years
• 7 Years
• 8 Years
• 12 Years

Solution

Let the age of Rohit = x years  Father's age = 32 years  Accordingly: 6x = 2(32) - 28 6x = 64 - 28 6x = 36 x = 6 Thus, Rohit is 6 years old. 

Q18. Five added to a one third of a number gives twice the number, then the number is

• 3
• 4
• 5
• 6

Solution

Q19. The marks scored by Parmeet in a math test are 11 more than twice the marks scored by Rita. If Parmeet scored 45, then the marks scored by Rita are:

• 39
• 17
• 56
• 34

Solution

Let marks scored by Rita = x Marks scored by Parmeet = 11 more than twice of x Marks scored by Parmeet = 11 + 2x = 45 => 2x = 34 => x = 17 Hence, marks scored by Rita = 17  

Q20. The solution of equation  5(p +1) + 4 = 34 is

• p = 4
• p = -3
• p = 7
• p = 5

Solution

5(p +1) + 4 = 345p + 5 + 4 = 345p + 9 = 34Transposing 9 to RHS, we get5p = 34 - 95p = 25Dividing both sides by 5, we getp = 5

Q21. The linear equation 5x - 5 = -10 is same as

• x - 1 = -2
• x - 1 = 10
• x - 5 = 2
• x - 1 = 2

Solution

5x - 5 = -10On dividing both sides of the equation by 5, we getx - 1 = -2 Hence, option (A)

Q22. The solution of the equation 4x + 5 = 29

• x = 6
• x = -6
• x = 0
• x = -3

Solution

4x + 5 = 29Transposing 5 to RHS4x = 29 - 54x = 24x = 6

Q23. P added to 4 gives 5 can be expressed as

• P - 4 = 5
• 4 - P = 5
• 5 - P = 4
• P + 4 = 5

Solution

P added to 4 means P + 4P added to 4 gives 5 means P + 4 = 5

Q24. The first step that we will use to separate variable in the linear equation15x = 11 is

• Transposing 15 to RHS
• Transposing 11 to LHS
• Diving both sides by 15
• Multiplying both sides with 15

Solution

15x = 11 If we will divide both sides by 15, the variable would be free of one termSo, first step is to divide both sides by 15.

Q25. The Ages of A and B are in the ratio of 5:3, after six years their ages will be in the ratio of 7:5. The present age of A is

• 5 years
• 10 years
• 15 years
• 20 years

Solution

Q26. Two angles add up to give 90^o. Smaller angle is 12^o more than half of the bigger angle. The bigger angle is 

• 60^o
• 50^o
• 54^o
• 64^o

Solution

Let the smaller angle be x Then the bigger angle = 90^o – x

Q27. Which of the following number cannot be multiplied on both sides?

• 1
• 0
• -1
• 2

Solution

0 cannot be multiplied on both sides.

Q28. For equation y + 8 =13, statement is

• Sum of 8 and 13 is y
• Sum of y and 8 is 13
• Sum of 13 and y is 8
• 8 times y is 13

Solution

Let one number be y y + 8 is 8 added to y  y + 8 = 13 can be stated as sum of y and 8 gives 13  

Q29. Leena bought pens which were 5 more than the number of pencils. The cost of one pencil be Rs.2. And that of a pen be Rs.3. If Leena spent Rs.65 to buy pens and pencils, then how many pencils did she buy?

• 7
• 10
• 15
• 12

Solution

Q30. A number when multiplied by 6 is increased by 45, then the number is

• 2
• 3
• 4
• 9

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