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Practice Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions based on the NCERT syllabus. Solve fresh and exam-oriented MCQs on equations, number problems, consecutive integers, age problems, and equation verification.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 5
Difficulty Level: Moderate
Based On: NCERT Syllabus
Introduction
Simple equations provide a systematic method for finding unknown quantities. By representing an unknown number with a variable, a statement can be converted into an equation and solved using appropriate operations.
For example, if a number increased by $8$ is $20$, we can represent it as:
$$x+8=20$$
Solving the equation gives:
$$x=12$$
In Practice Set 5, students will practise fresh questions involving number relationships, consecutive numbers, age situations, and equations with variables on both sides.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Forming equations from number statements
✔ Working with consecutive numbers
✔ Solving age-based equations
✔ Using inverse operations
✔ Verifying solutions
Why This Topic Is Important
Equations with unknown quantities on one or both sides help students develop stronger algebraic reasoning. These concepts are useful for solving mathematical puzzles, number problems, and real-life situations.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ NCERT-Based Practice
✔ Mathematics Revision
Q1. Solve the equation:
$$3x+5=x+17$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer:
B) $$6$$
Useful Concept
When the variable appears on both sides, first bring the variable terms to one side and the constant terms to the other side.
Solution
Given:
$$3x+5=x+17$$
Subtract $x$ from both sides:
$$3x-x+5=17$$
$$2x+5=17$$
Subtract $5$ from both sides:
$$2x=12$$
Divide by $2$:
$$x=6$$
Verification
Substitute $x=6$ into the original equation:
Left side:
$$3(6)+5=18+5=23$$
Right side:
$$6+17=23$$
Since:
$$23=23$$
the solution is correct.
Hence, the correct answer is:
B) $$6$$
Q2. Which equation represents the statement:
“Seven less than twice a number is 15”?
A) $$2x+7=15$$
B) $$2x-7=15$$
C) $$7x-2=15$$
D) $$2(x-7)=15$$
Answer:
B) $$2x-7=15$$
Useful Concept
“Twice a number” means $$2x$$, while “seven less than” means subtract $$7$$.
Solution
Let the number be:
$$x$$
Twice the number:
$$2x$$
Seven less than twice the number:
$$2x-7$$
According to the statement:
$$2x-7=15$$
Therefore, the correct equation is:
B) $$2x-7=15$$
We can solve it:
$$2x-7=15$$
Add $$7$$ to both sides:
$$2x=22$$
Divide by $$2$$:
$$x=11$$
Verification:
$$2(11)-7=22-7=15$$
Thus, the equation is correct.
Q3. The sum of three consecutive integers is 48. What is the middle integer?
A) $$14$$
B) $$15$$
C) $$16$$
D) $$17$$
Answer:
C) $416$$
Useful Concept
If the middle consecutive integer is $x$, the three consecutive integers can be represented as:
$$x-1,\ x,\ x+1$$
Solution
Let the middle integer be:
$$x$$
Then the three consecutive integers are:
$$x-1,\quad x,\quad x+1$$
Their sum is $48$:
$$x-1+x+x+1=48$$
Simplifying:
$$3x=48$$
Therefore:
$$x=16$$
Hence, the middle integer is:
$$16$$
Verification
The three integers are:
$$15,\ 16,\ 17$$
Their sum is:
$$15+16+17=48$$
Therefore, the answer is correct.
Hence, the correct answer is:
C) $$16$$
Q4. A father’s age is three times his son’s age. Their total age is 48 years. What is the son’s age?
A) $$10$$ years
B) $$12$$ years
C) $$14$$ years
D) $$16$$ years
Answer:
B) $$12$$ years
Useful Concept
If the son’s age is $$x$$, then three times his age is $$3x$$. The sum of their ages gives the equation.
Solution
Let the son’s age be:
$$x$$
Father’s age:
$$3x$$
Their total age is $48$:
$$x+3x=48$$
Therefore:
$$4x=48$$
Divide both sides by $4$:
$$x=12$$
Thus, the son’s age is:
$$12\text{ years}$$
Verification
Son’s age:
$$12$$
Father’s age:
$$3(12)=36$$
Total:
$$12+36=48$$
Therefore, the answer is correct.
Hence, the correct answer is:
B) $$12$$ years
Q5. The difference between a number and 9 is 17. What is the number?
A) $$8$$
B) $$17$$
C) $$26$$
D) $$28$$
Answer:
C) $$26$$
Useful Concept
“The difference between a number and 9” can be represented as:
$$x-9$$
Solution
Let the number be:
$$x$$
According to the question:
$$x-9=17$$
Add $9$ to both sides:
$$x=17+9$$
Therefore:
$$x=26$$
Verification
$$26-9=17$$
$$17=17$$
Thus, the solution is correct.
Hence, the correct answer is:
C) $$26$$
Important Formulas & Concepts
Variable on Both Sides
For an equation such as:
$$ax+b=cx+d$$
bring variable terms to one side and constants to the other side.
Three Consecutive Integers
If the middle integer is $x$:
$$x-1,\ x,\ x+1$$
Their sum is:
$$3x$$
Two Consecutive Integers
If the first integer is $x$:
$$x,\ x+1$$
Twice a Number
$$2x$$
Three Times a Number
$$3x$$
Difference
The difference between $x$ and $a$ is:
$$x-a$$
Age Problems
If one person’s age is $x$ and another person’s age is three times the first person’s age:
$$3x$$
Their combined age can be represented as:
$$x+3x=4x$$
Verification
Always substitute the obtained value into the original equation.
If both sides are equal, the solution is verified.
Related Practice Questions
Q1. Solve:
$$4x+3=2x+15$$
Q2. Write an equation for:
Six less than three times a number is 21.
Q3. The sum of three consecutive integers is 63. Find the middle integer.
Q4. A mother is twice her daughter’s age. Their total age is 45 years. Find their ages.
Q5. The difference between a number and 12 is 25. Find the number.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$4x+5=2x+17$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Which equation represents “three times a number decreased by 4 is 20”?
A) $$3x+4=20$$
B) $$3x-4=20$$
C) $$4x-3=20$$
D) $$3(x-4)=20$$
Q3. The middle of three consecutive integers whose sum is 75 is:
A) $$24$$
B) $$25$$
C) $$26$$
D) $427$4
Q4. If a father’s age is twice his son’s age and their total age is 54, the son’s age is:
A) $$16$$
B) $$18$$
C) $$20$$
D) $$22$$
Q5. The difference between a number and 15 is 21. The number is:
A) $$6$$
B) $$30$$
C) $$36$$
D) $$42$$
Exam Tips
✔ When variables appear on both sides, collect variable terms on one side.
✔ Use inverse operations carefully.
✔ For consecutive integers, remember the difference between successive integers is $1$.
✔ Define the variable clearly in age problems.
✔ Translate words such as “twice”, “three times”, “difference”, and “sum” correctly.
✔ Verify the answer using the original equation.
Quick Revision Notes
✔ Variable terms can be collected on one side.
✔ Three consecutive integers can be written as:
$$x-1,\ x,\ x+1$$
✔ Their sum is:
$$3x$$
✔ Twice a number:
$$2x$$
✔ Three times a number:
$$3x$$
✔ Difference between $x$ and $a$:
$$x-a$$
✔ Always verify the solution.
Common Mistakes Students Make
❌ Moving a variable term to the wrong side without changing the operation correctly.
❌ Confusing three consecutive integers with multiples of three.
❌ Forgetting to define the unknown age.
❌ Writing $x+2$ instead of $x+1$ for the next consecutive integer.
❌ Misinterpreting “difference”.
❌ Skipping verification.
Key Takeaways
✔ Variables can occur on both sides of an equation.
✔ Consecutive integers differ by $1$.
✔ Number relationships can be represented using equations.
✔ Age relationships can be solved using variables.
✔ Inverse operations help isolate the unknown.
✔ Verification confirms the correctness of the answer.
FAQs
Q. How do we solve an equation with variables on both sides?
Answer:
Bring all variable terms to one side and constants to the other side, then isolate the variable.
For example:
$$3x+5=x+17$$
gives:
$$2x=12$$
so:
$$x=6$$
Q. How are three consecutive integers represented?
Answer:
If the middle integer is $$x$$, they are:
$$x-1,\ x,\ x+1$$
Q. What does “twice a number” mean?
Answer:
If the number is $$x$$, twice the number is:
$$2x$$
Q. How do we represent “9 less than a number”?
Answer:
If the number is $$x$$, then 9 less than the number is:
$$x-9$$
Q. Why are equations useful in age problems?
Answer:
Equations allow us to represent relationships between ages using variables and solve for unknown ages systematically.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on equations with variables on both sides, consecutive integers, age relationships, and number-based problems.
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