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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, fractions, consecutive numbers, age problems, geometry, and real-life applications.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 11
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
Simple equations help us find unknown quantities by expressing relationships mathematically. An equation consists of two expressions connected by an equality sign, and both sides must remain equal during the solving process.
For example:
$$5x-6=24$$
Adding $6$ to both sides gives:
$$5x=30$$
and therefore:
$$x=6$$
Equations can also be used to solve problems involving consecutive numbers, ages, costs, lengths, and other real-life situations.
This Practice Set 11 contains 5 fresh MCQs designed to strengthen students’ equation-solving and application skills.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Forming equations from verbal statements
✔ Solving consecutive-number problems
✔ Applying equations to practical situations
✔ Verifying solutions
Why This Topic Is Important
Simple equations are one of the fundamental concepts of algebra. They help students translate mathematical statements and real-life situations into equations and determine unknown values logically.
A strong understanding of this topic is useful for geometry, word problems, and algebraic concepts in higher classes.
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:
$$10x-13=6x+15$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
C) $$7$$
Useful Concept
Bring all variable terms to one side and all constant terms to the other side.
Solution
Given:
$$10x-13=6x+15$$
Subtract $$6x$$ from both sides:
$$10x-6x-13=15$$
$$4x-13=15$$
Add $$13$$ to both sides:
$$4x=28$$
Divide by $$4$$:
$$x=7$$
Verification
Left side:
$$10(7)-13=70-13=57$$
Right side:
$$6(7)+15=42+15=57$$
Therefore:
$$57=57$$
Hence, the solution is correct.
Correct Answer: B) $$7$$
Correction: The value is $$7$$, which corresponds to option B, not C.
Therefore, the correct answer is:
B) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{9}+2=7$$
A) $$36$$
B) $$45$$
C) $$54$$
D) $$63$$
Answer:
B) $$45$$
Useful Concept
First isolate the fractional term and then multiply by its denominator.
Solution
Given:
$$\frac{x}{9}+2=7$$
Subtract $$2$$ from both sides:
$$\frac{x}{9}=5$$
Multiply both sides by $$9$$:
$$x=45$$
Verification
$$\frac{45}{9}+2=5+2=7$$
Therefore, the solution is correct.
Correct Answer: B) $$45$$
Q3. The sum of two consecutive integers is 57. What is the larger integer?
A) $$27$$
B) $$28$$
C) $$29$$
D) $$30$$
Answer:
C) $$29$$
Useful Concept
Two consecutive integers differ by $$1$$. If the smaller integer is $$x$$, the larger is:
$$x+1$$
Solution
Let the smaller integer be:
$$x$$
The larger integer is:
$$x+1$$
Their sum is $$57$$:
$$x+(x+1)=57$$
Simplify:
$$2x+1=57$$
Subtract $$1$$:
$$2x=56$$
Divide by $$2$$:
$$x=28$$
Therefore, the larger integer is:
$$28+1=29$$
Verification
$$28+29=57$$
Hence, the answer is correct.
Correct Answer: C) $$29$$
Q4. A number is 4 less than five times another number. If the larger number is 31, what is the smaller number?
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer:
C) $$7$$
Useful Concept
“Five times a number” means $$5x$$, and “4 less than” means:
$$5x-4$$
Solution
Let the smaller number be:
$$x$$
The larger number is:
$$5x-4$$
Given that the larger number is $$31$$:
$$5x-4=31$$
Add $$4$$ to both sides:
$$5x=35$$
Divide by $$5$$:
$$x=7$$
Therefore, the smaller number is:
$$7$$
Verification
$$5(7)-4=35-4=31$$
Thus, the answer is correct.
Correct Answer: C) $$7$$
Q5. A rectangular garden has a perimeter of 70 m. Its length is 5 m more than its breadth. What is the breadth?
A) $$12$$ m
B) $$15$$ m
C) $$17$$ m
D) $$20$$ m
Answer:
B) $15$ m
Useful Concept
For a rectangle:
$$P=2(l+b)$$
If breadth is $$x$$, length is:
$$x+5$$
Solution
Let the breadth be:
$$x\text{ m}$$
Then the length is:
$$x+5\text{ m}$$
Given:
$$P=70\text{ m}$$
Using:
$$2(l+b)=70$$
we get:
$$2[(x+5)+x]=70$$
Simplify:
$$2(2x+5)=70$$
$$4x+10=70$$
Subtract $$10$$:
$$4x=60$$
Divide by $$4$$:
$$x=15$$
Therefore, the breadth is:
$$15\text{ m}$$
Verification
Length:
$$15+5=20\text{ m}$$
Perimeter:
$$2(20+15)=2(35)=70\text{ m}$$
Therefore, the answer is correct.
Correct Answer: B) $$15$$ m
Important Formulas & Concepts
Equation with Variables on Both Sides
For:
$$ax+b=cx+d$$
collect all variable terms on one side and constants on the other.
Fractional Equation
For:
$$\frac{x}{a}+b=c$$
we get:
$$\frac{x}{a}=c-b$$
and therefore:
$$x=a(c-b)$$
Two Consecutive Integers
If the smaller integer is $$x$$:
$$x,\ x+1$$
Five Times a Number
$$5x$$
Four Less Than Five Times a Number
$$5x-4$$
Rectangle Perimeter
$$P=2(l+b)$$
Verification
Substitute the obtained value into the original equation or condition to check the answer.
Related Practice Questions
Q1. Solve:
$$9x-5=5x+23$$
Q2. Find $$x$$:
$$\frac{x}{8}+4=11$$
Q3. The sum of two consecutive integers is 73. Find both integers.
Q4. A number is 3 less than four times another number. If the larger number is 29, find the smaller number.
Q5. A rectangular field has a perimeter of 80 m. Its length is 10 m more than its breadth. Find its dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$8x-7=5x+14$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Find $$x$$:
$$\frac{x}{7}+3=9$$
A) $$36$$
B) $$42$$
C) $$48$$
D) $$56$$
Q3. Two consecutive integers have a sum of 65. The larger integer is:
A) $$31$$
B) $$32$$
C) $$33$$
D) $$34$$
Q4. A number is 5 less than three times another number. If the larger number is 25, the smaller number is:
A) $$8$$
B) $$9$$
C) $$10$$
D) $$11$$
Q5. A rectangle has perimeter 62 m and its length is 5 m more than its breadth. Its breadth is:
A) $$12$$ m
B) $$13$$ m
C) $$14$$ m
D) $$15$$ m
Exam Tips
✔ Remember that consecutive integers differ by $$1$$.
✔ Collect variable terms carefully when they occur on both sides.
✔ Isolate fractions before multiplying by the denominator.
✔ Translate phrases such as “five times” and “four less” correctly.
✔ For rectangles, use:
$$P=2(l+b)$$
✔ Define the variable clearly in word problems.
✔ Always verify the final answer.
Quick Revision Notes
✔ Variables on both sides:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}+b=c$$
✔ Consecutive integers:
$$x,\ x+1$$
✔ Five times a number:
$$5x$$
✔ Four less than five times a number:
$$5x-4$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ Verification:
Substitute the obtained answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive integers as numbers differing by $$2$$.
❌ Forgetting to isolate the fraction.
❌ Confusing “four less than five times” with $$4-5x$$.
❌ Using the wrong rectangle perimeter formula.
❌ Making arithmetic mistakes while simplifying.
❌ Forgetting to verify the final result.
Key Takeaways
✔ Simple equations help determine unknown quantities.
✔ Consecutive integers differ by $$1$$.
✔ Variables can occur on both sides of an equation.
✔ Fractions can be handled using inverse operations.
✔ Real-life situations can be converted into equations.
✔ Rectangle perimeter problems can be solved using simple equations.
✔ Verification confirms the correctness of a solution.
FAQs
Q. What are consecutive integers?
Answer:
Consecutive integers are numbers that follow one another and differ by $$1$$.
For example:
$$12,\ 13,\ 14$$
Q. How are two consecutive integers represented?
Answer:
If the smaller integer is $$x$$, the two integers are:
$$x,\ x+1$$
Q. What does “five times a number” mean?
Answer:
If the number is $$x$$, five times the number is:
$$5x$$
Q. What does “4 less than five times a number” mean?
Answer:
It is represented by:
$$5x-4$$
Q. What is the perimeter of a rectangle?
Answer:
The perimeter is:
$$P=2(l+b)$$
where $$l$$ is length and $$b$$ is breadth.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh and challenging practice on equations with variables on both sides, fractional equations, consecutive integers, number relationships, and rectangle-based application questions.
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