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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, exam-oriented MCQs on equations, fractions, consecutive numbers, ages, 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: 13
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
A simple equation is a mathematical statement in which an unknown quantity is represented by a variable. The equality sign shows that the expressions on both sides have the same value.
For example:
$$7x-5=30$$
Adding $5$ to both sides:
$$7x=35$$
Therefore:
$$x=5$$
Simple equations can be used to solve problems involving numbers, ages, money, lengths, and other quantities.
This Practice Set 13 contains 5 fresh MCQs designed to strengthen equation-solving skills and mathematical reasoning.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Finding unknown numbers
✔ Working with consecutive odd numbers
✔ Solving age-related problems
✔ Applying equations to geometry
✔ Verifying solutions
Why This Topic Is Important
Simple equations are a fundamental part of algebra. They help students translate statements and real-life situations into mathematical equations and find unknown quantities logically.
The concepts learned here also prepare students for more advanced algebraic equations 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:
$$12x-15=8x+17$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
B) $$8$$
Useful Concept
When the variable appears on both sides, collect the variable terms on one side and the constants on the other.
Solution
Given:
$$12x-15=8x+17$$
Subtract $8x$ from both sides:
$$12x-8x-15=17$$
$$4x-15=17$$
Add $$15$$ to both sides:
$$4x=32$$
Divide by $$4$$:
$$x=8$$
Verification
Left side:
$$12(8)-15=96-15=81$$
Right side:
$$8(8)+17=64+17=81$$
Therefore:
$$81=81$$
Hence, the solution is correct.
Correct Answer: C) $$8$$
Correction: The value is $$8$$, which corresponds to option C, not B.
Therefore, the correct answer is:
C) $$8$$
Q2. Find the value of $$x$$:
$$\frac{x}{7}-4=5$$
A) $$49$$
B) $$56$$
C) $$63$$
D) $$70$$
Answer:
C) $$63$$
Useful Concept
First isolate the fractional term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{7}-4=5$$
Add $4$ to both sides:
$$\frac{x}{7}=9$$
Multiply both sides by $$7$$:
$$x=63$$
Verification
$$\frac{63}{7}-4=9-4=5$$
Therefore, the solution is correct.
Correct Answer: C) $$63$$
Q3. The sum of three consecutive odd numbers is 105. What is the middle number?
A) $$33$$
B) $$35$$
C) $$37$$
D) $$39$$
Answer:
B) $$35$$
Useful Concept
Three consecutive odd numbers can be represented as:
$$x,\ x+2,\ x+4$$
Solution
Let the smallest odd number be:
$$x$$
Then the three numbers are:
$$x,\quad x+2,\quad x+4$$
Their sum is $$105$$:
$$x+(x+2)+(x+4)=105$$
Simplify:
$$3x+6=105$$
Subtract $$6$$:
$$3x=99$$
Divide by $$3$$:
$$x=33$$
Therefore, the numbers are:
$$33,\ 35,\ 37$$
The middle number is:
$$35$$
Verification
$$33+35+37=105$$
Hence, the answer is correct.
Correct Answer: B) $$35$$
Q4. A number is 7 more than twice another number. If the larger number is 35, what is the smaller number?
A) $$12$$
B) $$13$$
C) $$14$$
D) $$15$$
Answer:
B) $$14$$
Useful Concept
If the smaller number is $$x$$, twice the number is $$2x$$. Seven more than twice the number is:
$$2x+7$$
Solution
Let the smaller number be:
$$x$$
The larger number is:
$$2x+7$$
Given:
$$2x+7=35$$
Subtract $$7$$:
$$2x=28$$
Divide by $$2$$:
$$x=14$$
Therefore, the smaller number is:
$$14$$
Verification
$$2(14)+7=28+7=35$$
Hence, the answer is correct.
Correct Answer: C) $$14$$
Correction: The calculated answer is $$14$$, which corresponds to option C, not B.
Therefore, the correct answer is:
C) $$14$$
Q5. A rectangular field has a perimeter of 86 m. Its length is 7 m more than its breadth. What is the length of the field?
A) $$18$$ m
B) $$20$$ m
C) $$22$$ m
D) $$24$$ m
Answer:
B) $$22$$ m
Useful Concept
The perimeter of a rectangle is:
$$P=2(l+b)$$
If the breadth is $$x$$, then the length is:
$$x+7$$
Solution
Let the breadth be:
$$x\text{ m}$$
Then the length is:
$$x+7\text{ m}$$
Given:
$$P=86\text{ m}$$
Therefore:
$$2[(x+7)+x]=86$$
Simplify:
$$2(2x+7)=86$$
$$4x+14=86$$
Subtract $$14$$:
$$4x=72$$
Divide by $$4$$:
$$x=18$$
Therefore, breadth is:
$$18\text{ m}$$
Length:
$$18+7=25\text{ m}$$
Verification
$$2(25+18)=2(43)=86\text{ m}$$
Therefore, the length is:
$$25\text{ m}$$
Important Correction: $$25$$ m is not included in the given options. Therefore, the original options are incorrect.
Correct Answer: $$25$$ m
Important Formulas & Concepts
Equation with Variables on Both Sides
For:
$$ax+b=cx+d$$
collect variable terms on one side and constants on the other.
Fractional Equation
For:
$$\frac{x}{a}-b=c$$
we get:
$$\frac{x}{a}=b+c$$
Therefore:
$$x=a(b+c)$$
Three Consecutive Odd Numbers
If the smallest number is $$x$$:
$$x,\ x+2,\ x+4$$
Twice a Number Plus 7
$$2x+7$$
Rectangle Perimeter
$$P=2(l+b)$$
Verification
Substitute the obtained value into the original equation or condition to confirm the answer.
Related Practice Questions
Q1. Solve:
$$13x-10=9x+22$$
Q2. Find $$x$$:
$$\frac{x}{8}-3=6$$
Q3. The sum of three consecutive odd numbers is 123. Find the middle number.
Q4. A number is 9 more than twice another number. If the larger number is 41, find the smaller number.
Q5. A rectangular field has a perimeter of 94 m. Its length is 9 m more than its breadth. Find its dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$10x-7=6x+21$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$$:
$$\frac{x}{9}+4=10$$
A) $$45$$
B) $$54$$
C) $$63$$
D) $$72$$
Q3. Three consecutive odd numbers have a sum of 117. The middle number is:
A) $$37$$
B) $$39$$
C) $$41$$
D) $$43$$
Q4. A number is 5 more than twice another number. If the larger number is 31, the smaller number is:
A) $$11$$
B) $$12$$
C) $$13$$
D) $$14$$
Q5. A rectangle has perimeter 74 cm. Its length is 7 cm more than its breadth. The length is:
A) $$18$$ cm
B) $$20$$ cm
C) $$22$$ cm
D) $$24$$ cm
Exam Tips
✔ Collect variable terms carefully.
✔ Isolate the fraction before multiplying by its denominator.
✔ Remember that consecutive odd numbers differ by $$2$$.
✔ Translate phrases such as “twice”, “more than”, and “less than” carefully.
✔ Use:
$$P=2(l+b)$$
for rectangle perimeter problems.
✔ Check whether the calculated answer matches the options.
✔ Always verify the final answer.
Quick Revision Notes
✔ Variables on both sides:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}-b=c$$
✔ Three consecutive odd numbers:
$$x,\ x+2,\ x+4$$
✔ Twice a number plus 7:
$$2x+7$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive odd numbers as numbers differing by $$1$$.
❌ Forgetting to add a constant before removing a fraction.
❌ Confusing “7 more than twice” with “7 times”.
❌ Using the wrong perimeter formula.
❌ Selecting an option without checking the calculated result.
❌ Not verifying the final answer.
Key Takeaways
✔ Simple equations help determine unknown values.
✔ Variables can occur on both sides of an equation.
✔ Fractions can be solved through inverse operations.
✔ Consecutive odd numbers differ by $$2$$.
✔ Number relationships can be represented algebraically.
✔ Geometry problems can be converted into simple equations.
✔ Verification helps confirm the correctness of an answer.
FAQs
Q. How are three consecutive odd numbers represented?
Answer:
If the smallest number is $$x$$, they are:
$$x,\ x+2,\ x+4$$
Q. What does “7 more than twice a number” mean?
Answer:
If the number is $$x$$, it means:
$$2x+7$$
Q. What is the rectangle perimeter formula?
Answer:
$$P=2(l+b)$$
Q. How do we solve $$\frac{x}{7}-4=5$$?
Answer:
Add $$4$$:
$$\frac{x}{7}=9$$
Then multiply by $$7$$:
$$x=63$$
Q. What should we do if the calculated answer is not among the options?
Answer:
Recheck the calculation and the question. If the calculation is correct, the options may contain an error. The mathematically correct answer should be reported.
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 odd numbers, number relationships, and rectangle-based applications.
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