NCERT Exemplar Solutions
Class 7 - Mathematics

Unit 4: Simple Equations

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

(a) If smaller number is x, the other number is ________ (use sum).

(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 ________.

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 ________.

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 ________ marks.

(b) The equation formed is ________.

(c) The solution of the equation is ________.

(d) Marks obtained by Abha are ________.

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

(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 ________.

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

(a) The worth of x coins of ₹5 each ________.

(b) The worth of x coins of ₹2 each ________.

(c) The equation formed is ________.

(d) There are ________ 5 rupee coins and ________ 2 rupee coins.

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 ₹52,000 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 ________.

If z + 3 = 5, then z = ________.

________ is the solution of the equation 3x − 2 = 7.

________ is the solution of 3x + 10 = 7.

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

In integers, 4x − 1 = 8 has ________ solution.

In natural numbers, 4x + 5 = −7 has ________ solution.

In natural numbers, x − 5 = −5 has ________ solution.

In whole numbers, x + 8 = 12 − 4 has ________ solution.

If 5 is added 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 ________.

x + 7 = 10 has the solution ________.

x − 0 = ________; when 3x = 12.

x − 1 = ________; when 2x = 2.

x − ________ = 15; when x/2 = 6.

The solution of the equation x + 15 = 19 is ________.

Finding the value of a variable in a linear equation that ________ the equation is called a ________ of the equation.

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.

If 9/5 x = 18/5, then x = ________.

If 3 − x = −4, then x = ________.

If x − 1/2 = −1/2, then x = ________.

If 1/6 − x = 1/6, then x = ________.

If 10 less than a number is 65, then the number is ________.

If a number is increased by 20, it becomes 45. Then the number is ________.

If 84 exceeds another number by 12, then the other number is ________.

If x − 7/8 = 7/8, then x = ________.

5 is the solution of the equation \(3x + 2 = 17\).

\(\dfrac{9}{5}\) is the solution of the equation \(4x − 1 = 8\).

\(4x − 5 = 7\) does not have an integer as its solution.

One third of a number added to itself gives 10, can be represented as \(\dfrac{x}{3} + 10 = x\).

\(\dfrac{3}{2}\) is the solution of the equation \(8x − 5 = 7\).

If \(4x − 7 = 11\), then \(x = 4\).

If 9 is the solution of variable x in the equation \(\dfrac{5x − 7}{2} = y\), then the value of y is 28.

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

13 subtracted from twice of a number gives 3.

One-fifth of a number is 5 less than that number.

A number is 7 more than one-third of itself.

Six times a number is 10 more than the number.

If 10 is subtracted from half of a number, the result is 4.

Subtracting 5 from p, the result is 2.

Five times a number increased by 7 is 27.

Mohan is 3 years older than Sohan. The sum of their ages is 43 years.

If 1 is subtracted from a number and the difference is multiplied by 1/2, the result is 7.

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

The sum of twice a number and 4 is 18.

The age of Sohan Lal is four times that of his son Amit. If the difference of their ages is 27 years, find the age of Amit.

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

Seven times a number is 12 less than thirteen times the same number. Find the number.

The interest received by Karim is ₹30 more than that of Ramesh. If the total interest received by them is ₹70, find the interest received by Ramesh.

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

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.

Two times a number increased by 5 equals 9. Find the number.

9 added to twice a number gives 13. Find the number.

1 subtracted from one-third of a number gives 1. Find the number.

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

After 20 years, Manoj will be 5 times as old as he is now. Find his present age.

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.

If 45 is added to half a number, the result is triple the number. Find the number.

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.

In a bag, the number of one rupee coins is three times the number of two rupee coins. If the worth of the coins is ₹120, find the number of 1 rupee coins.

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 had thought of?

One of the two numbers is twice the other. The sum of the numbers is 12. Find the numbers.

The sum of three consecutive integers is 5 more than the smallest of the integers. Find the integers.

A number when divided by 6 gives the quotient 6. What is the number?

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.

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.

The sum of two consecutive multiples of 2 is 18. Find the numbers.

Two complementary angles differ by 20°. Find the angles.

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

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.

Two-third of a number is greater than one-third of the number by 3. Find the number.

A number is as much greater than 27 as it is less than 73. Find the number.

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?

Twice a number added to half of itself equals 24. Find the number.

Thrice a number decreased by 5 exceeds twice the number by 1. Find the number.

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.

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

Look at this riddle:
If 7 pencils would cost you ₹6 more than 5 pencils, then find the cost of your 10 pencils.

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?

Radha got ₹17,480 as her monthly salary and over-time. Her salary exceeds the over-time by ₹10,000. What is her monthly salary?

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.

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

(a) Remove two of these matchsticks to make a valid equation:
IX − VI = V

(b) Move one matchstick to make the equation valid. Find two different solutions.

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

If i + 69 = 70, then i = ?

If 8u = 6u + 8, then u = ?

If 4a = −5a + 45, then a = ?

If 4q + 5 = 17, then q = ?

If −5t − 60 = −70, then t = ?

If (1/4)s + 98 = 100, then s = ?

If (5/3)p + 9 = 24, then p = ?

If 3c = c + 12, then c = ?

If 3(k + 1) = 24, then k = ?

For riddle answer: substitute the number for the letter it equals.

The three scales below are perfectly balanced if • = 3. What are the values of Δ and *?

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.