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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: 14
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
Simple equations are mathematical statements in which an unknown quantity is represented by a variable. By applying the same operation to both sides of an equation, we can determine the value of the unknown.
For example:
$$4x+7=31$$
Subtracting $$7$$ from both sides:
$$4x=24$$
Therefore:
$$x=6$$
Simple equations can also be used to solve problems involving numbers, ages, money, lengths, and geometrical measurements.
This Practice Set 14 contains 5 fresh and challenging MCQs covering different applications of simple equations.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Working with consecutive integers
✔ Forming equations from verbal statements
✔ Solving age-related problems
✔ Applying equations to geometry
✔ Verifying solutions
Why This Topic Is Important
Simple equations develop algebraic reasoning and help students translate information from words into mathematical expressions.
They are an important foundation for solving word problems and understanding 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:
$$13x-11=9x+21$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
C) $$8$$
Useful Concept
When the variable occurs on both sides, bring all variable terms to one side and constants to the other.
Solution
Given:
$$13x-11=9x+21$$
Subtract $$9x$$ from both sides:
$$13x-9x-11=21$$
$$4x-11=21$$
Add $$11$$:
$$4x=32$$
Divide by $$4$$:
$$x=8$$
Verification
Left side:
$$13(8)-11=104-11=93$$
Right side:
$$9(8)+21=72+21=93$$
Therefore:
$$93=93$$
Hence, the solution is correct.
Correct Answer: C) $$8$$
Q2. Find the value of $$x$$:
$$\frac{x}{8}+5=12$$
A) $$48$$
B) $$54$$
C) $$56$$
D) $$64$$
Answer:
C) $$56$$
Useful Concept
First isolate the fractional term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{8}+5=12$$
Subtract $$5$$ from both sides:
$$\frac{x}{8}=7$$
Multiply both sides by $$8$$:
$$x=56$$
Verification
$$\frac{56}{8}+5=7+5=12$$
Therefore, the solution is correct.
Correct Answer: C) $$56$$
Q3. The sum of two consecutive integers is 91. What is the smaller integer?
A) $$44$$
B) $$45$$
C) $$46$$
D) $$47$$
Answer:
B) $$45$$
Useful Concept
Two consecutive integers differ by $$1$$.
If the smaller integer is $$x$$, the larger integer is:
$$x+1$$
Solution
Let the smaller integer be:
$$x$$
Then the larger integer is:
$$x+1$$
Their sum is $$91$$:
$$x+(x+1)=91$$
Simplify:
$$2x+1=91$$
Subtract $$1$$:
$$2x=90$$
Divide by $$2$$:
$$x=45$$
Therefore, the smaller integer is:
$$45$$
Verification
$$45+46=91$$
Hence, the answer is correct.
Correct Answer: B) $45$
Q4. A number is 6 less than three times another number. If the larger number is 30, what is the smaller number?
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Answer:
C) $$12$$
Useful Concept
Three times a number is $$3x$$. Six less than this is:
$$3x-6$$
Solution
Let the smaller number be:
$$x$$
The larger number is:
$$3x-6$$
Given:
$$3x-6=30$$
Add $$6$$:
$$3x=36$$
Divide by $$3$$:
$$x=12$$
Therefore, the smaller number is:
$$12$$
Verification
$$3(12)-6=36-6=30$$
Therefore, the answer is correct.
Correct Answer: C) $$12$$
Q5. A rectangular garden has a perimeter of 78 m. Its length is 7 m more than its breadth. What is the breadth?
A) $$14$$ m
B) $$15$$ m
C) $$16$$ m
D) $$17$$ m
Answer:
B) $$15$$ 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 length:
$$x+7\text{ m}$$
Given:
$$P=78\text{ m}$$
Therefore:
$$2[(x+7)+x]=78$$
Simplify:
$$2(2x+7)=78$$
$$4x+14=78$$
Subtract $$14$$:
$$4x=64$$
Divide by $$4$$:
$$x=16$$
Therefore, the breadth is:
$$16\text{ m}$$
Verification
Length:
$$16+7=23\text{ m}$$
Perimeter:
$$2(23+16)=2(39)=78\text{ m}$$
Therefore, the answer is correct.
Correction: The calculated answer is $$16$$ m, which corresponds to option C, not B.
Hence, the correct answer is:
C) $$16$$ m
Important Formulas & Concepts
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:
$$\frac{x}{a}=c-b$$
Therefore:
$$x=a(c-b)$$
Two Consecutive Integers
If the smaller integer is $$x$$:
$$x,\ x+1$$
Three Times a Number
$$3x$$
Six Less Than Three Times a Number
$$3x-6$$
Rectangle Perimeter
$$P=2(l+b)$$
Verification
Substitute the obtained value into the original equation or condition to check the result.
Related Practice Questions
Q1. Solve:
$$14x-9=10x+23$$
Q2. Find $$x$$:
$$\frac{x}{9}+3=8$$
Q3. The sum of two consecutive integers is 105. Find the integers.
Q4. A number is 8 less than four times another number. If the larger number is 40, find the smaller number.
Q5. A rectangular field has a perimeter of 90 m. Its length is 5 m more than its breadth. Find its dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$11x-6=7x+22$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$$:
$$\frac{x}{5}+4=11$$
A) $$30$$
B) $$35$$
C) $$40$$
D) $$45$$
Q3. Two consecutive integers have a sum of 101. The smaller integer is:
A) $$49$$
B) $$50$$
C) $$51$$
D) $$52$$
Q4. A number is 7 less than three times another number. If the larger number is 29, the smaller number is:
A) $10$
B) $11$
C) $12$
D) $13$
Q5. A rectangle has perimeter 82 cm. Its length is 7 cm more than its breadth. The breadth is:
A) $$16$$ cm
B) $$17$$ cm
C) $$18$$ cm
D) $$19$$ cm
Exam Tips
✔ Collect variable terms carefully.
✔ Isolate fractional terms before multiplying.
✔ Remember that consecutive integers differ by $$1$$.
✔ Translate “three times” and “six less” correctly.
✔ Use:
$$P=2(l+b)$$
for rectangle perimeter questions.
✔ Define the variable before forming an equation.
✔ Verify the final answer before selecting an option.
Quick Revision Notes
✔ Variables on both sides:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}+b=c$$
✔ Consecutive integers:
$$x,\ x+1$$
✔ Three times a number:
$$3x$$
✔ Six less than three times:
$$3x-6$$
✔ 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 “six less than three times” with $$6-3x$$.
❌ Using an incorrect rectangle perimeter formula.
❌ Selecting an answer without checking the calculation.
❌ Skipping verification.
Key Takeaways
✔ Simple equations help find unknown quantities.
✔ Variables can occur on both sides of an equation.
✔ Fractional equations can be solved using inverse operations.
✔ Consecutive integers differ by $$1$$.
✔ Verbal relationships can be represented algebraically.
✔ Rectangle problems can be converted into equations.
✔ Verification ensures the final answer is correct.
FAQs
Q. What are consecutive integers?
Answer:
Consecutive integers are numbers that differ by exactly $$1$$.
For example:
$$24,\ 25,\ 26$$
Q. How are two consecutive integers represented?
Answer:
If the smaller integer is $$x$$, they are:
$$x,\ x+1$$
Q. What does “6 less than three times a number” mean?
Answer:
If the number is $$x$$, the expression is:
$$3x-6$$
Q. What is the perimeter formula for a rectangle?
Answer:
$$P=2(l+b)$$
Q. How do we solve $$\frac{x}{8}+5=12$$?
Answer:
Subtract $$5$$:
$$\frac{x}{8}=7$$
Then multiply by $$8$$:
$$x=56$$
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 applications.
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