Questions based on Simple Equations 

Extra Questions Based on chapter-4 Simple Equations 

This page consists of questions based on chapter 4 Simple Equations of class 7 Maths and has MCQ-based questions with detailed explanations. to check out the solution of any MCQ click on the Answer. do solve NCERT textbook questions with the help of NCERT solutions for class 7 Maths. 

Questions for Chapter-4 Simple Equations  Set-1 

Chapter – 04

Q1. Vidya’s mother’s age is 5 years more than the three times of Vidya’s present age. Find Vidya’s present age, if his mother is 44 years old.

(a) 10 years (b) 16 years

(c) 13 years (d) 18 years

Ans.1. (c) Suppose Vidya’s age is year

Then 3 y + 5 = 44

⇒ 3 y = 44 – 5 = 39

⇒ y = 13 years

Q2. The sum of four times a number and 12 is 36. Find the number?

(a) 7 (b) 4

(c) 6 (d) 5

Ans.2. (c) If the unknown number is taken to be x,

then four times the number is 4 x and

the sum of 4x and 12 is 36

that is, 4 x + 12 = 36

To solve this equation, we transpose 12 to R.H.S,

So that 4x = 36 –12 = 24

⇒ x = 6

Q3. A shopkeeper sells apples in two types of boxes, one small and one large. A large box contains double as many as small boxes plus 6 loose mangoes. The number of mangoes in a large box is given to be 100. Then the number of apples in small box is

(a) 47 (b) 48

(c) 49 (d) 35

Ans.3. (a) Let small box contain ‘m’ mangoes

Then according to the given equation 2m + 6 = 100

⇒ m = 100-6/2 = 94/2 = 47

Q4. Which of the following is correct? Choose the answer from the code given below

I. The sum of numbers x and 4 is 9

In equation form, it is represented as x + 4 = 9

II. Seven times M plus 7 you 77

In equation form, it is represented as 7 M + 7 = 77

III. If you add 3 to one third of Z, you get 30.

In equation form, it is represented as 3+ Z/3 = 30

Code:

(a) I and II (b) II and III

(c) All are correct (d) All are incorrect

Ans.4. (c) All are correct.

I. x + 4 = 9

II. Seven times M is 7 M.

Sum of 7 M and 7 is 7M + 7

The sum is 77.

Hence the equation is 7 M + 7 = 77

III. One third of Z is Z/3

Sum of Z/3  and 3 is Z/3 + 3 .

The sum is 30.

Hence the equation is Z/3 + 3 =30

Q5. What are the values of p and m if 3p –1 = 23 and 6m – 2 = 34

(a) p = 6, m = 7 (b) p = 8, m = 6

(c) p = 6, m = 6 (d) p = 4, m = –6

Ans.5. (b) 3p –1 = 23 ⇒ 3p = 23 + 1 ⇒ p=8

and 6 m –2 = 34 ⇒ 6m = 36 ⇒ m = 6

Q6. Which of the following is correct?

I. 7m + 19/2=13 then m =1/2

II. 5t + 28 = 3, then t = –5

III. 5x –2 = 8, then x = 3

Code :

(a) I, III  (b) II & III

(c) I & II (d) All are correct

Ans.6. (c) I.7m= 13 - 19/2 = 26-19/2 = 7/2 

m=1/2

II. 5t = 3–28 = –25 ⇒ t = – 5

III. 5x –2 = 8 ⇒ 5x = 10, x = 2

Hence, I and II are correct.

Q7. Sachin says that he has 6 books more than the 6 times of the books Priyanka has. Sachin has 42 books. How many books does Priyanka have?

(a) 8 (b) 6

(c) 9 (d) 10

Ans.7. (b) Let Priyanka has p books.

Then according to the question 6p + 6 = 42 ⇒ p = 6

Q8. The teachers tell the class that the lowest marks obtained by a student in her class are one-forth the highest marks plus 8 is 33. What is the highest score?

(a) 90 (b) 100

(c) 60 (d) 200

Ans.8. (b) Let H be the highest marks.

Then according to the question, H/4 + 8 = 33 ⇒ H = (33 – 8) 4 = 100

Q9. In an isosceles triangle, the base angles are equal and the vertex angle is 50°. What are the values of base angles of the triangles?

(a) 60 ° (b) 45°

(c) 65° (d) None of these

Ans.9. (c) Let each of the base angle is θ.

Then equation is 2θ + 15 = 180

⇒ θ = 180-50/2 = 130/2 = 65°

Q10. Laxmi takes away 7 from 5/2  of the number, the result is 11/2  . Then the number is

(a) 11/2 (b) 5/2

(c) 11 (d) 5

Ans.10. (d) Let numbers is x

then equation is 5/2 x -7=11/2

⇒ 5x/2=11/2 +7=25/2

⇒ x = 5

Q11. The solution of 3(b + 2)–(b – 8) = 3(b + 8) is

(a) –10 (b) 10

(c) 2 (d) –3

Ans.11. (a) 3 (b + 2) – (b –8) = 3(b +8)

3b + 6 – b + 8 = 3b + 24

2b + 14 = 3b + 24

b = –10

Q12. A student has to secure 35% marks to pass. He got 80 marks and failed by 60 marks. Find the maximum marks.

(a) 100 (b) 200

(c) 300 (d) 400

Ans.12. (d) 35/100 x = 80 + 60

35/100 x= 140  ⇒ x = 400

Q13. There were only two candidates who participated in an election. One contestant got 62% votes and was elected by a margin of 144 votes. The total number of votes were

(a) 500 (b) 600

(c) 700 (d) 800

Ans.13. (b) Elected candidate got  62x/100 votes. Other candidates got 38x / 100 votes. We have,

⇒62x/100-38x/100=144

24x/100=144⇒ x = 600

Q14. In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x –2) trees yield 180 nuts per year. If the average yield per year of all trees be 100, then find x.

(a) 4 (b) 3

(c) 2 (d) 1

Ans.14. (a)

Q15. The average of 11, 12, 13, 14 and x is 13. The value of x is

(a) 17 (b) 21

(c) 15 (d) None of these

Ans.15. (c)

11+12+13+14+x/5 =13

x = 65 – 50

x = 15

Q16. The average of three numbers is 60. The first is 1/4 th of the sum of the other two . The first number is

(a) 24 (b) 36

(c) 48 (d) 72

Ans.16. (b) Let a, b and c are three numbers.

a+b+c /3 =60

a + b +c = 180

and a=1/4(b+c) = 1/4(180-a)

4a = 180 –a

a= 180/5 =36

Q17. The ratio between two numbers is 3 : 5. If each number is increased by 4, the ratio becomes 2:3. Find the numbers.

(a) 12,20 (b) 18,30

(c) 24,40 (d) 15,25

Ans.17. (a) Let the numbers be 3x, 5x

3x+4/ 5x+4 =2/3 

9x + 12 = 10x + 8

x = 4

⇒The numbers are 3 × 4, 5 × 4 = 12, 20

Q18. 4 is added to a number and the sum is multiplied by 5. If 20 is subtracted from the product and the difference is divided by 8, the result is equal to 10. Find the number.

(a) 16 (b) 12

(c) 8 (d) 20

Questions for Chapter-4 Simple Equations  Set-2

Ans.18. (a) Let the number be x.

(x+4) × 5-20/8 =10

5x + 20 – 20 = 80

x = 16

Q19. One number is 3 less than the two times of the other. If their sum is increased by 7, the result is 37. Find the numbers.

(a) 9,11 (b) 11,13

(c) 11,19 (d) 9, 13

Ans.19. (c) Let one number = x

Other number = 2x – 3

(x + 2x –3)+ 7 = 37

3x = 33

x = 11

Q20. 1/2 is subtracted from a number and the difference is multiplied by 4, then 25 is added to the product that sum is divided by 3, the result is equal to 10. Find the number.

(a) 3/5 (b) 7/4

(c) 6/7 (d) None of these

Ans.20. (b) Let the number be x.

⇒ 4x – 2 + 25 = 30

⇒ 4x = 7

⇒ x= 7/4 

Q21. The present age of A is twice that of B. 30 years from now, age of A will be 1½  times that of B. Find the present ages of A and B respectively.

(a) 60, 30 (b) 30, 60

(c) 40, 50 (d) 50, 40

Ans.21. (a) Present age: A = 2x, B = x

After 30 years: A = 2x + 30, B = x + 30

So 2x + 30 = 1½ (x + 30)

⇒ 4x + 60 = 3x + 90

⇒ x = 30

Q22. The present age of a man is 3 times that of his son. Six years ago, the age of the man was four times that of his son. Find the ratio of their ages six years later.

(a) 4 : 3 (b) 3 : 4

(c) 2 : 5 (d) 5 : 2

Ans.22. (d) Let present age of son = x years

Present age of man = 3x

Six years ago

Age of man = 3x –6

Age of son = x –6

3x –6= 4(x –6)

3x –6= 4x –24

x = 18

Six years after

Age of man = 3 × 18 + 6 = 60

Age of son = 18 + 6 = 24

Required Ratio = 60 : 24 = 5 : 2

Q23. The total cost of three prizes is Rs. 2550. If the value of the second prize is 3/4 th of the first and the value of 3rd prize is 1/2 of the second prize, find the value of the first prize.

(a) Rs 900 (b) Rs 1500

(c) Rs 1200 (d) Rs 450

Ans.23. (c) Let first prize = x

Second prize =3/4x

Third Prize = 1/2  3x/4= 3x/8

x+3x/4+3x/8=2550

17x/8 = 2550.

x = 1200

Q24. The sum of 4 consecutive integers is 70. Then the greatest among them is

(a) 19 (b) 23

(c) 17 (d) 16

Ans.24. (a) The consecutive integers are x, x +1, x+2, x+ 3.

x + x+ 1 + x + 2+ x+ 3 = 70

⇒ 4x + 6 = 70

⇒ 4x = 64

⇒ x = 16

⇒ Greatest number = x + 3 = 16 + 3 = 19.

Q25. If two supplementary angles are differ by 44° then one of the angle is

(a) 102° (b) 65°

(c) 112° (d) 72°

Ans.25. (c) The angles are x, x – 44°

So x + x – 44° = 180°

2x = 224°

x = 112°

07 - Mat

Unit - N.A

Questions for Chapter-4 Simple Equations  Set-3

Q1. If one-third of x plus 9 is 12. Then the value of x is

(a) 1 (b) 9

(c) 3 (d) 12

Ans.1. (b) One third of x = x/3

According to question, x/3 +9 = 12

x/3 = 12 - 9 = 3

x/3 =  3/1, x = 3 3 = 9

x = 9

Q2. The sum of four times x and 6 is 34, its statement in the form of

equation is

(a) 4x - 6 = 34 (b) 4x - 34 = 6

(c) 4x + 6 = 34 (d) x/4 + 6 = 34

Ans.2. (c) Four times of x = 4x

Then, according to question

4x+6 = 34

Q3. What is the value of p, if (5p -2) = (1 +2p)

(a) 2 (b) 1

(c) 3 (d) 4

Ans.3. (b) (5p -2) = (1 +2p)

5p - 2p = 1 + 2

3p = 3, p = 3/3 = 1

Q4. The equation 3p +6 = 21 in the statement form is

(a) Two times of p and plus 6 is 21.

(b) Three times of p and plus 6 is 21.

(c) Four times of p and plus 6 is 21.

(d) Three times of x and plus 6 is 21.

Ans.4. (b) Three times of p = 3p

3p plus six is 21, 3p +6 = 21

Q5. What is the value of q, if 2q + 6 = 12

(a) 2 (b) 1

(c) 3 (d) -1

Ans.5. (c) The given equation is 2q + 6 = 12

subtracting 6 on both the sides

2q + 6 - 6 = 12 -6,

2q = 6 ( dividing by 2 on both the sides)

q = 3

Q6. What is the value of a, if a/3 = 7/4

Ans.6. (a)

Q7. Solution of 2y + 5/2 = 37/2 is

(a) 6    (b) 8

(c) 10  (d) 12

Ans.7. (b) 2y + 5/2 = 37/2

2y = 37/2 - 5/2 (transposing 5/2 to R.H.S)

2y = 37-5 / 2 = 32/2 =16

2Y = 16

Y =16/2 = 8

Q8. -4(x - 2) = 16, the value of x is

(a) 2 (b) -1

(c) 1 (d) -2

Ans.8. (d) -4(x - 2) = 16

Dividing by (-4) on both the sides, we have

(x – 2) = -4

x = -4 +2 transposing (-2) to R.H.S

x = -2

Q9. The sum of three consecutive integers is 21. The least integer is ……..

(a) 9 (b) 6

(c) 18 (d) 21

Let three consecutive integers be x, x+1 and x+2.

Ans. 9.(b)

According to question

x + x+1 +x+2 = 21

3x + 3 = 21

3x = 21 -3 = 18

3x = 18, x = 18/3 = 6

Q10. Shanu’s father’s age is 6 years more than three times shanu’s age.

Find shanu’s age, if his father is 48 years old.

(a) 14 (b) 12

(c) 16 (d) 18

Ans.10. (a) Let shanu’s age be x.

According to question

Three times of shanu’s age + 6 = shanu’s father age’s

3x + 6 = 48

3x = 48 - 6 = 42

3x = 42, x = 14

Q11. The length of a reactangle is twice of its breadth. If the perimeter of

the reactangle is 18 cm, then the area of its reactangle is…….

(a) 72 sq cm (b) 36 sq cm

(c) 18 sq cm (d) 49 sq cm

Ans.11. (c) Let breadth of the given reactangle is x.

Then length of its reactangle = 2x

perimeter = 2(length + breadth)

2(2x + x) = 18

3x = 18/2 = 9

x = 9/3 = 3 cm

breadth = 3 cm

length = 2 3 = 6 cm

Area of the given reactangle = length breadth

area = 6 3 = 18 sq cm

Q12. What is the value of t? If 4 + 3(t + 2) = 10.

(a) 1 (b) 2

(c) 0 (d) -1

Ans.12. (c) 4 + 3(t + 2) = 10

3(t + 2) = 10 – 4 (transposing 4 to R.H.S)

3(t + 2) = 6

dividing by 3 on both the sides

(t + 2) = 2

t = 2 - 2 = 0

t = 0

Q13. What is the number one third of which added to 5 gives 6?

(a) 4 (b) 3

(c) 1 (d) 2

Ans.13. (b) Let the number be x.

According to question

x/3 + 5= 6 

x/3 = 6 – 5

x/3 = 1, x = 3 × 1 = 3

The required number is 3.

Q14. Sachin scored twice as many runs as rahul. Together, their runs fell two short of a double century. How many runs did each one score?

(a) 122 and 61 (b) 132 and 66

(c) 112 and 56 (d) 66 and 132

Ans.14. (b) Let rahul’s score be x.

Then sachin’s score will be 2x.

According to question

x + 2x = 198

3x = 198

x = 198/3 = 66

and 2x = 2 66 = 132

Hence sachin and rahul score’s are 132 and 66 respectively.

Q15. Isha subtracts thrice the number of notebooks she has from 44, he find the result 5. What is the number?

(a) 14 (b) 13

(c) 12 (d) 15

Ans.15. (b) Let the required number be x.

According to question

44 – 3x = 5

- 3x = 5 – 44 (transposing 44 to R.H.S)

- 3x = -39

dividing by (-3) on both the sides

x = 13

Q16. Average of 1, 3, 5, x, 8 is 9. The value of x will be

(a) 18 (b) 27

(c) 8 (d) 28

Ans.16. (d) Average = (sum of observation)/ number of observation

9 = 1+3+5+x+8 / 5

x+17/5 = 9/1

x + 17 = 45

x = 45 – 17 = 28

Q17. If two complementary angles are differ by , then one of the angle

is ……

(a) 58° (b) 36°

(c) 46° (d) 30°

Ans.17. (a) Iet the angles are x, (x - 26 ° )

x + x - 26° = 90°

2x = 90° + 26° =  116°

x = 116°/2 = 58°

Q18. In an isosceles triangle, the base angles are equal. The vertex angle is . What are the base angles of the triangle?

(a) 75° (b) 65°

(c) 45° (d) 55°

Ans.18. (a) Let the base angle of given triangle is x.

We know that sum of all angles of a triangle is 180°.

x + x + 30° = 180°

2x =180° - 30° = 150°

x = 150° /2 = 75°

Q19. Two-fifth of a number minus 5 gives 3. The number is

(a) 10 (b) 30

(c) 20 (d) 40

Ans.19. (c) Let required number be x.

According to question,

2x/5-5 =3

2x/5=3+5= 8

2x/5= 8/1

x =8 × 5 /2 = 4 × 5 = 20

Q20. Uttam thinks of a number. If he takes away 5 from 7/2 of the number,

the result is 11/2 . The number will be

(a) 4 (b) 3

(c) 5 (d) 6

Ans.20. (b) Let the required number be x.

According to question,

Q21. Amit‘s father is 69 years old. He is 4 years older than five times Amit’s

age. What is Amit’s age?

(a) 12 (b) 17

(c) 14 (d) 13

Ans.21. (d) Let amit’s age be x.

Then according to question

five times amit’s age + 4 = amit’s father age

5x + 4 = 69

5x = 69 – 4 = 65, x = 65/5 = 13

Q22. When I subtract 7 from twice a number, the result was 9. What is the

number?

(a) 6 (b) 8

(c) 9 (d) 7

Ans.22. (b) Let the number be x.

According to question,

2x – 7 = 9

2x = 9 + 7 =16

x = 16/2 = 8

Q23. If two supplementary angles are differ by then one of the angle is

(a) 116°  (b) 117°

(c) 118°  (d) 54°

Ans.23. (b) Let the angles are x and (x - 54° ).

Then, x + x - 54° =118°

2x = 180° + 54° = 234°

x = 234° /2 =117°

Q24. If (3x - 7/2 ) = (x + 3/2). Then the value of x is ……

(a) 3/2  (b) 5/2

(c) 7/2  (d) 9/2

Ans.24. (b) (3x - 7/2  ) = (x + 3/2 )

3x – x = 3/2 + 7/2 = 3+7/2

2x = 10/2 = 5

x = 5/2

Q25. If ( 7x/3 - 4/3= x/2 +3/2 ), then the value of x is …….

(a) 16/11 (b) 15/11

(c) 17/10 (d) 17/11

Ans.25. (d)

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