**NCERT Exemplar Problems Class 7 Maths – Simple Equations**

**Question 1:**

**Solution:**

**Question 2:
**If

**a**and

**b**are positive integers, then the solution of the equation

**ax = b**will always be a

(a) positive number

(b) negative number

(c) 1

(d) 0

**Solution:**

(a) Given equation is ax = b

On dividing the equation by a, we get

x =

Now, if a and b are positive integers, then the solution of the equation is also positive number as division of two positive integers is also a positive number.

**Question 3:**

**Which of the following is not allowed in a given equation?**

(a) Adding the same number to both sides of the equation.

(b) Subtracting the same number from both sides of the equation.

(c) Multiplying both sides of the equation by the same non-zero number.

(d) Dividing both sides of the equation by the same number.

**Solution:**

**(d)**Dividing both sides of the equation by the same non-zero number is allowed in a given equation, division of any number by zero is not allowed as set division of number by zero is not defined.

**Note**If we add same number to both sides of the equation while adding subtracting, then there will be no change in the given equation.

**Question 4:
**The solution of which of the following equations is neither a positive fraction nor an integer?

(a) 2x + 6 = 0

(b) 3x – 5=0

(c) 5x – 8 = x + 4

(d) 4x + 7 = x + 2

**Solution:**

**Question 5:
**The equation which can not be solved in integers is

(a) 5y — 3 = — 18

(b) 3x-9=0

(c) 3z + 8 = 3 + z

(d) 9y + 8 = 4y-7

**Solution:**

**Question 6:
**If 7x + 4 = 25, then

**x**is equal to

(a)

(b)

(c) 2

(d) 3

**Solution:**

**Question 7:
**The solution of the equation 3x + 7 = – 20 is

(a)

(b) -9

(c) 9

(d)

Solution:

Solution:

**Question 8:
**The value of y for which the expressions (y -15) and (2y +1) become equal is

(a) 0 (b) 16 (0 8 (d)-16

**Solution:**

**Question 9:
**If k + 7 = 16, then the value of 8k – 72 is

(a) 0

(b) 1

(c) 112

(d) 56

**Solution:**

**Question 10:
**If 43m = 0.086, then the value of

**m**is

(a) 0.002

(b) 0.02

(c) 0.2

(d) 2

**Solution:**

**Question 11:
**x exceeds 3 by 7, can be represented as

(a) x + 3 = 2

(b) x + 7 = 3

(c) x – 3 = 7

(d) x – 7 = 3

**Solution:**

The given statement means x is 7 more than 3.

So, the equation is x – 7 = 3

We can also write it as x – 3 = 7.

**Question 12:**

The equation having 5 as a solution is

(a) 4x + 1 = 2

(b) 3 – x = 8

(c) x – 5 = 3

(d) 3 + x = 8

**Solution:**

**Question 13:
**The equation having – 3 as solution is

(a) x + 3 = 1

(b) 8 + 2x = 3

(c) 10 + 3x = 1

(d) 2x + 1 = 3

**Solution:**

**Question 14:
**Which of the following equations can be formed starting with x = 0?

(a) 2x + 1 = -1

(b) + 5=7

(c)3x-1 = -1

(d)3x-1=1

**Solution:**

**Question 15:
**Which of the following equations cannot be formed using the equation x -V.

(a) 2x + 1 = 15 (b) 7x -1 = 50 (c) x – 3 = 4 (d) y-1=0

**Solution:**

**Question 16:
**If = 3, then the value of 3x + 2 is 2

(a) 20 (b) 11 (c) (d)8

**Solution:**

**Question 17:
**Which of the following numbers satisfy the equation – 6 + x = – 12 ?

(a) 2 (b) 6 (c) -6 (d) – 2

**Solution:**

**Question 18:
**Shifting one term from one side of an equation to another side with a change of sign is known as

(a) commutativity

(b) transposition

(c) distributivity

(d) associativity

**Solution:**

(b) Transposition means shifting one term from one side of an equation to another side with a change of sign.

**Fill in the blanks
**In questions 19 to 48 , fill in the blanks to make the statements true.

**Question 19:
**The sum of two numbers is 60 and their difference is 30.

(a) If smaller number is x, the other number is_________ .

(b) The difference of numbers in term of x is________ .

(c) The equation formed is______ .

(d) The solution of the equation is_______ .

(e) The numbers are_______ and_________ .

**Solution:**

Given, the sum of two numbers is 60 and difference is 30.

(a) If the smaller number is x, then the other number is (60- x), since the sum of both numbers is 60.

(b) Given, one number = x [from (a)]

Then, other number = (60 – x)

∴ Difference = (60 – x) – x = 60 – 2x

**Question 20:
**Sum of two numbers is 81. One is twice the other______.

(a) If smaller number is x, the other number is _

(b) The equation formed is______ .

(c) The solution of the equation is________ .

(d) The numbers are_________ and_________ .

**Solution:**

(a) We are given that one number is twice the other.

If smaller number is x, then the other number is 2x.

(b) We are given that sum of two numbers is 81. So, the equation will be

**Question 21:
**In a test, Abha gets twice the marks as that of Palak. Two times Abha’s marks and three times Palak’s marks make 280.

(a) If Palak gets x marks, Abha gets________.

(b) The equation formed is______ .

(c) The solution of the equation is________ .

(d) Marks obtained by Abha are_______ .

**Solution:**

(a) If Palak gets x marks, then Abha gets twice the marks as that of Palak, i.e. 2x,

(b) Two times of Abha’s marks = 2 (2x) = Ax and three times the Palak marks = 3(x) = 3x

Now, two times Abha’s marks and three times Palak’s marks make 280.

So, the equation formed is 4x+ 3x= 280.

(c) Solve the equation for x,

**Question 22:
**The length of a rectangle is two times its breadth. Its perimeter is 60cm.

(a) If the breadth of rectangle is x cm, the length of the rectangle is_______ .

(b) Perimeter in terms of x is______ .

(c) The equation formed is________ .

(d) The solution of the equation is________ .

**Solution:**

(a) It is given that the length of the rectangle is two times its breadth.

∴ Length =

**2x**

**cm**

(b) Perimeter of rectangle = 2 (Length + Breadth) = 2 (2x+ x)

**Question 23:**

In a bag, there are Rs. 5 and Rs. 2 coins. If they are equal in number and their worth is Rs. 70, then

(a) The worth of x coins of Rs. 5 each_______ .

(b) The worth of x coins of Rs. 2 each________ .

(c) The equation formed is________ .

(d) There are______ Rs. 5 coins and_________ Rs. 2 coins.

**Solution:**

Let number of coins of Rs. 5 = x

Then, number of coins of Rs. 2 = x

(a) Number of coins of Rs.5 = x

So, the worth of Rs. 5 of x coins = Rs.5 x x = Rs. 5x

(b) Similarly, the worth of 12 of x coins = Rs. 2x

**Question 24:
**In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ? 2000 and ? 1000, respectively. If the total prize money is Rs. 52000, then show that

(a) If 1st prizes are x in number the number of 2nd prizes are__________ .

(b) The total value of prizes in terms of x are_________ .

(c) The equation formed is_______ .

(d) The solution of the equation is________ .

(e) The number of 1st prizes are_________ and the number of 2nd prizes are________ .

**Solution:**

Given, number of prizes = 30

Total prize money = Rs. 52000, 1st and 2nd prizes are worth Rs. 2000 and Rs. 1000, respectively.

(a) 1st prizes are x in number, the number of 2nd prizes are

**(30-x)**, because total number of prizes are 30.

(b)Total value of prizes in terms of x are

**2000x+ 1000 (30- x).**

**Question 25:
**If

**z**+ 3 = 5, then

**z**= ________ .

**Solution:**

**Question 26:
**_________ is the solution of the equation 3x – 2 = 7.

**Solution:**

**Question 27:
**_______ is the solution of 3x +10 = 7.

**Solution:**

**Question 28:
**If

**2x**+ 3 = 5, then value of 3x + 2 is.

**Solution:**

**Question 29:
**In integers, 4x – 1 = 8 has________ solution.

**Solution:**

**In natural numbers, 4x + 5 = – 7 has ______ solution.**

Question 30:

Question 30:

**Solution:**

**Question 31:
**In natural numbers,

**x –**5 = – 5 has______ solution.

**Solution:**

**In whole numbers,**

Question 32:

Question 32:

**x**+ 8 = 12 – 4 has solution.

**Solution:**

**If 5 is addes to three times a number, it becomes the same as 7 is subtracted from four times the same number. This fact can be represented as ______.**

Question 33:

Question 33:

**Solution:**

Let the number be x.

Now, 5 is added to 3 times the number 5 + 3x.

It is same as 7 is subtracted from 4 times the number, i.e. Ax – 7.

So, the equation formed is

**5+ 3x= 4x- 7**.

**Question 34:
**

**x**+ 7 = 10 has the solution ______.

**Solution:**

**Question 35:
**x – 0 = ______ when 3x=12.

**Solution:**

**Question 36:
**x – 1 = ______ when 2x=2.

**Solution:**

**Question 37:
x** – ______ =15; when = 6

**Solution:**

**Question 38:
**The solution of the equation x + 15 = 19 is.

**Solution:**

**Question 39:
**Finding the value of a variable in a linear equation that______________ the equation is called a_______ of the equation.

**Solution:**

Finding the value of a variable in a linear equation that

**satisfies**the equation is called a

**roo**t of the equation.

**Question 40:
**Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ___________ of the term.

**Solution:**

Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the

**sign**of the term.

**Question 41:**

**Solution:**

**Question 42:
**If 3 – x =-4

**,**then

**x = ___.**

**Solution:**

**Question 43:**

**Solution:**

**Question 44:**

**Solution:**

**Question 45:
**If 10 less than a number is 65, then the number is_________.

**Solution:**

Let the number be x.

Then, the equation will be x – 10 = 65

;

**Question 46:
**If a number is increased by 20, it becomes 45. Then, the number is _________.

**Solution:**

Let the number be x.

If it is increased by 20, it becomes (x + 20),

**Question 47:
**If 84 exceeds another number by 12, then the other number is _________.

**Solution:**

**Question 48:**

**Solution:**

**True / False
**In questions 49 to 55, state whether the statements are True or False.

**Question 49:
**5 is the solution of the equation 3x + 2 = 17.

**Solution:**

**Question 50:
** is the solution of the equation 4x – 1 = 8.

**Solution:**

**Question 51:
**4x – 5 = 7 does not have an integer as its solution.

**Solution:**

**Question 52:****
**One-third of a number added to itself gives 10, can be represented as + 10 = x.

**Solution:**

**False**

Let the number be x.

Then, the equation formed is + x = 10

**Question 53:
** is the solution of the equation 8x – 5 = 7.

**Solution:**

**Question 54:
**If 4x – 7 = 11, then x = 4.

**Solution:**

**Question 55:
**If 9 is the solution of variable x in the equation = y, then the value of y is 28.

**Solution:**

**Question 56:
**Match each of the entries in Column I with the appropriate entries in Column II.

**Solution:**

In questions from 57 to 67, express each of the given statements as an equation.

**Question 57:
**13 subtracted from twice of a number gives 3.

**Solution:**

Let the number be x.

13 is subtracted from twice of a number i.e, 2x -13 and it results 3.

So, the equation formed is 2x -13 = 3

**Question 58:
**One-fifth of a number is 5 less than that number,

**Solution:**

Let the number be x.

**Question 59:
**A number is 7 more than one-third of itself.

**Solution:**

**Question 60:**

Six times a number is 10 more than the number.

**Solution:**

Let the number be x.

Then, 6 times of a number = 6x

So, the equation formed is 6x = 10 + x

**Question 61:
**If 10 is subtracted from half of a number, the result is 4.

**Solution:**

**Question 62:
**Subtracting 5 from

**p,**the result is 2.

**Solution:**

Subtract 5 from p i.e. p – 5 and its results 2. Hence, the equation formed is p – 5 = 2.

**Question 63:
**Five times a number increased by 7 is 27.

**Solution:**

Let the number be x. Then, five times of number be 5x.

Since, it is increased by 7 i.e. 5x + 7 and it gives result 27.

Hence, the equation formed is 5x + 7 = 27

**Question 64:
**Mohan is 3 years older than Sohan. The sum of their ages is 43 years.

**Solution:**

Let age of Sohan be x yr. Then, the age of Mohan is (x + 3)yr.

∴ Sum of their ages = 43

So, the equation formed is x + {x + 3) = 43

**Question 65:
**If 1 is subtracted from a number and the difference is multiplied by ½ the result is 7.

**Solution:**

**Question 66: **

A number divided by 2 and then increased by 5 is 9.

**Solution:**

**Question 67:
**The sum of twice a number and 4 is 18.

**Solution:**

Let the number be x.

Then, sum of twice of a number and 4 gives result 18. Hence, 2x + 4 = 18 is the equation.

**Question 68:
**The age of Sohan Lai is four times that of his son Amit. If the difference of their ages is 27 years, find the age of Amit.

**Solution:**

**Question 69:
**A number exceeds the other number by 12. If their sum is 72, find the numbers.

**Solution:**

**Question 70:
**Seven times a number is 12 less than thirteen times the same number. Find the number.

**Solution:**

**Question 71:****
**The interest received by Karim is Rs. 30 more than that of Ramesh. If the total interest received by them is Rs. 70, find the interest received by Ramesh

**Solution:**

**Question 72:
**Subramaniam and Naidu donate some money in a Relief Fund. The amount paid by Naidu is Rs. 125 more than that of Subramaniam. If the total money paid by them is Rs. 975, find the amount of money donated by Subramaniam.

**Solution:**

**Question 73:
**In a school, the number of girls is 50 more than the number of boys. The total number of students is 1070. Find the number of girls.

**Solution:**

**Question 74:
**Two times a number increased by 5 equals 9. Find the number.

**Solution:**

;

**Question 75:
**9 added to twice a number gives 13. Find the number.

**Solution:**

**Question 76:
**1 subtracted from one-third of a number gives 1. Find the number.

**Solution:**

**Question 77:
**After 25 years, Rama will be 5 times as old as he is now. Find his present age.

**Solution:**

**Question 78:
**After 25 years, Manoj will be 5 times as old as he is now. Find his present age.

**Solution:**

**Question 79:
**My younger sister’s age today is 3 times what it will be 3 years from now minus 3 times what her age was 3 years ago. Find her present age.

**Solution:**

**Question 80:
**If 45 is added to half a number, the result is triple the number. Find the number.

**Solution:**

**Question 81:
**In a family, the consumption of wheat is 4 times that of rice. The total consumption of the two cereals is 80 kg. Find the quantities of rice and wheat consumed in the family.

**Solution:**

**Question 82:
**In a bag, the number of one rupee coins is three times the number of two rupees coins. If the worth of he coins is ? 120, find the number of 1 rupee coins.

**Solution:**

**Question 83:
**Anamika thought of a number. She multiplied it by 2, added 5 to the product and obtained 17 as the result. What is the number she has thought of?

**Solution:**

**Question 84:
**One of the two numbers is twice the other. The sum of the numbers is 12. Find the numbers.

**Solution:**

**Question 85:
**The sum of three consecutive integers is 5 more than the smallest of the integers. Find the integers.

**Solution:**

Let one number be x. Then, the next two consecutive numbers will be x + 1 and x + 2. Sum of these three numbers = x + (x + 1) + (x + 2) = 3x + 3

**Question 86:
**A number when divided by 6 gives the quotient 6. What is the number?

**Solution:**

**Question 87:
**The perimeter of a rectangle is 40 m. The length of the rectangle is 4 m less than 5 times its breadth. Find the length of the rectangle.

**Solution:**

**Question 88:
**Each of the 2 equal sides of an isosceles triangle is twice as large as the third side. If the perimeter of the triangle is 30 cm, find the length of each side of the triangle.

**Solution:**

Let third side of an isosceles triangle be x. Then, two other equal sides are twice.

So, the both equal sides are 2x and 2x.

We know that, perimeter of a triangle is sum of all sides of the triangle.

**Question 89:
**The sum of two consecutive multiples of 2 is 18. Find the numbers.

**Solution:**

**Question 90:
**Two complementary angles differ by 20°. Find the angles.

**Solution:**

**Question 91:
**150 has been divided into two parts such that twice the first part is equal to the second part. Find the parts.

**Solution:**

Let one part be x, then other part will be 2x as second part is twice the first part.

Since, 150 has been divided into above two parts.

**Question 92:
**In a class of 60 students, the number of girls is one third the number of boys. Find the number of girls and boys in the class.

**Solution:**

As per the given information in the question, the total number of students in the class = 60. Let x be the number of boys in the class.

Then, the number of girls in the class =

**Question 93:
**Two-third of a number is greater than one-third of the number by 3. Find the number.

**Solution:**

**Question 94:
**A number is as much greater than 27 as it is less than 73. Find the number.

**Solution:**

**Question 95:
**A man travelled two fifth of his journey by train, one third by bus. One-fourth by car and the remaining 3 km on foot. What is the length of his total journey?

**Solution:**

**Question 96:
**Twice’ a number added to half of itself equals 24. Find the number.

**Solution:**

**Question 97:
**Thrice a number decreased by 5 exceeds twice the number by 1. Find the number.

**Solution:**

**Question 98:
**A girl is 28 years younger than her father. The sum of their ages is 50 years. Find the ages of the girl and her father.

**Solution:**

**Question 99:
**The length of a rectangle is two times its width. The perimeter of the rectangle is 180 cm. Find the dimensions of the rectangle.

**Solution:**

**Question 100:
**Look at this riddle?

If she answers the riddle correctly how ever will she pay for the pencils ?

**Solution:**

**Question 101:
**In a certain examination, a total of 3768 students secured first division in the years 2006 and 2007. The number of first division in 2007 exceeded those in 2006 by 34. How many students got first division in 2006?

**Solution:**

Let the number of students who got first division in year 2006 be x. Since, the number of first division in year 2007 exceeded those in year 2006 by 34, therefore the number of students who got first division in year 2007 will be (x + 34).

It is given that total number of students who got first division in years 2006 and 2007 is 3768.

**Question 102:
** Radha got Rs. 17480 as her monthly salary and overtime. Her salary exceeds the overtime by Rs. 10000. What is her monthly salary?

**Solution:**

**Question 103:
**If one side of a square is represented by 18x – 20 and the adjacent side is represented by 42 – 13x, find the length of the side of the square.

**Solution:**

**Question 104:
**Follow the directions and correct the given incorrect equation, written in Roman numerals:

**Solution:**

**Question 105:
**What does a duck do when it flies upside down? The answer to this riddle is hidden in the equation given below :

**Solution:**

**Question 106:**

**Solution:**

**Question 107:
**The given figure represents a weighing balance. The weights of some objects in the balance are given. Find the weight of each square and the circle.

**Solution:**