NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 4: Simple Equations

Problems and Solutions

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.