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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, number relationships, perimeter, age problems, and practical applications.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 9
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
A simple equation is a mathematical statement containing an unknown quantity represented by a variable. The equality sign indicates that the expressions on both sides have the same value.
For example:
$$5x-8=27$$
To find the value of $$x$$, we use inverse operations while maintaining equality on both sides.
Simple equations can also be used to solve practical problems involving numbers, ages, lengths, costs, and perimeters.
This Practice Set 9 contains 5 fresh MCQs designed to strengthen equation-solving and application-based reasoning.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Forming equations from word statements
✔ Solving consecutive-number problems
✔ Applying equations to geometry problems
✔ Verifying the final answer
Why This Topic Is Important
Simple equations form an important foundation of algebra. They help students convert real-life situations into mathematical equations and find unknown quantities logically.
Strong knowledge of equations also prepares students for 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:
$$9x-7=4x+28$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer:
C) $$7$$
Useful Concept
When the variable occurs on both sides, collect all variable terms on one side and constants on the other side.
Solution
Given:
$$9x-7=4x+28$$
Subtract $$4x$$ from both sides:
$$9x-4x-7=28$$
$$5x-7=28$$
Add $$7$$ to both sides:
$$5x=35$$
Divide by $$5$$:
$$x=7$$
Verification
Left side:
$$9(7)-7=63-7=56$$
Right side:
$$4(7)+28=28+28=56$$
Therefore:
$$56=56$$
Hence, the solution is correct.
Correct Answer: C) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{6}+4=9$$
A) $$24$$
B) $$30$$
C) $$36$$
D) $$42$$
Answer:
B) $$30$$
Useful Concept
First isolate the fractional term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{6}+4=9$$
Subtract $$4$$ from both sides:
$$\frac{x}{6}=5$$
Multiply both sides by $$6$$:
$$x=30$$
Verification
$$\frac{30}{6}+4=5+4=9$$
Therefore, the solution is correct.
Correct Answer: B) $$30$$
Q3. The sum of three consecutive even numbers is 78. What is the smallest number?
A) $$22$$
B) $$24$$
C) $$26$$
D) $$28$$
Answer:
B) $$24$$
Useful Concept
Three consecutive even numbers can be represented as:
$$x,\ x+2,\ x+4$$
Solution
Let the smallest even number be:
$$x$$
Then the next two even numbers are:
$$x+2,\quad x+4$$
Their sum is $$78$$:
$$x+(x+2)+(x+4)=78$$
Simplify:
$$3x+6=78$$
Subtract $$6$$:
$$3x=72$$
Divide by $$3$$:
$$x=24$$
Therefore, the smallest number is:
$$24$$
Verification
The numbers are:
$$24,\ 26,\ 28$$
Their sum is:
$$24+26+28=78$$
Hence, the answer is correct.
Correct Answer: B) $$24$$
Q4. The length of a rectangle is 7 cm more than its breadth. If its perimeter is 54 cm, what is its breadth?
A) $$8$$ cm
B) $$9$$ cm
C) $$10$$ cm
D) $$11$$ cm
Answer:
B) $$10$$ cm
Useful Concept
For a rectangle:
$$P=2(l+b)$$
If the breadth is $$x$4, then the length is $$x+74$.
Solution
Let the breadth be:
$$x\text{ cm}$$
Then the length is:
$$x+7\text{ cm}$$
Given perimeter:
$$54\text{ cm}$$
Using:
$$P=2(l+b)$$
we get:
$$2[(x+7)+x]=54$$
Simplify:
$$2(2x+7)=54$$
$$4x+14=54$$
Subtract $$14$$:
$$4x=40$$
Divide by $$4$$:
$$x=10$$
Therefore, the breadth is:
$$10\text{ cm}$$
Verification
Length:
$$10+7=17\text{ cm}$$
Perimeter:
$$2(17+10)=2(27)=54\text{ cm}$$
Therefore, the answer is correct.
Correct Answer: C) $$10$$ cm
Correction: The calculated value is $10$ cm, which corresponds to option C, not B.
Hence, the correct answer is:
C) $$10$$ cm
Q5. Riya has ₹80 more than twice the amount of money that Neha has. If Riya has ₹240, how much money does Neha have?
A) ₹60
B) ₹70
C) ₹80
D) ₹90
Answer:
C) ₹80
Useful Concept
If Neha has ₹$$x$$, twice her amount is ₹$$2x$$. ₹80 more than this is:
$$2x+80$$
Solution
Let the amount Neha has be:
$$₹x$$
Riya has:
$$₹(2x+80)$$
Given that Riya has ₹240:
$$2x+80=240$$
Subtract ₹80:
$$2x=160$$
Divide by $$2$$:
$$x=80$$
Therefore, Neha has:
$$₹80$$
Verification
$$2(80)+80=160+80=240$$
Hence, the answer is correct.
Correct Answer: C) ₹80
Important Formulas & Concepts
Variable 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:
$$\frac{x}{a}=c-b$$
and therefore:
$$x=a(c-b)$$
Three Consecutive Even Numbers
If the smallest even number is $$x$$:
$$x,\ x+2,\ x+4$$
Perimeter of Rectangle
$$P=2(l+b)$$
where:
- $$l$$ = length
- $$b$$ = breadth
Twice a Number
$$2x$$
$k$ More Than Twice a Number
$$2x+k$$
Verification
Substitute the obtained value into the original equation to confirm that both sides are equal.
Related Practice Questions
Q1. Solve:
$$8x-6=3x+29$$
Q2. Solve:
$$\frac{x}{7}+3=10$$
Q3. The sum of three consecutive even numbers is 96. Find the numbers.
Q4. The length of a rectangle is 6 cm more than its breadth. Its perimeter is 52 cm. Find its dimensions.
Q5. A person has ₹50 more than twice another person’s money. The first person has ₹250. Find the second person’s money.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$7x-8=4x+16$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$$:
$$\frac{x}{5}+6=12$$
A) $$20$$
B) $$25$$
C) $$30$$
D) $$35$$
Q3. Three consecutive even numbers have a sum of 90. The smallest number is:
A) $$26$$
B) $$28$$
C) $$30$$
D) $432$$
Q4. A rectangle has perimeter 64 cm. Its length is 8 cm more than its breadth. The breadth is:
A) $$10$$ cm
B) $$12$$ cm
C) $$14$$ cm
D) $416$$ cm
Q5. Twice a number plus 10 is 50. The number is:
A) $$15$$
B) $$20$$
C) $$25$$
D) $$30$$
Exam Tips
✔ Collect variable terms on one side before solving.
✔ When fractions are present, isolate the fraction first.
✔ Consecutive even numbers differ by $$2$$.
✔ Use $$x,\ x+2,\ x+4$$ for three consecutive even numbers.
✔ Remember the rectangle perimeter formula:
$$P=2(l+b)$$
✔ Translate “twice”, “more than”, and “less than” carefully.
✔ Always verify the final value.
Quick Revision Notes
✔ General equation:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}+b=c$$
✔ Three consecutive even numbers:
$$x,\ x+2,\ x+4$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ Twice a number:
$$2x$$
✔ ₹80 more than twice $$x$$:
$$2x+80$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive even numbers as numbers differing by $$1$$.
❌ Forgetting to isolate the fraction before multiplying.
❌ Using the wrong rectangle perimeter formula.
❌ Confusing “twice a number plus 80” with “80 times the number”.
❌ Moving terms across the equality sign incorrectly.
❌ Skipping verification.
Key Takeaways
✔ Simple equations help find unknown quantities.
✔ Variables can occur on both sides.
✔ Fractional equations can be solved using inverse operations.
✔ Three consecutive even numbers differ by $$2$$.
✔ Geometry problems can be converted into equations.
✔ Money-related situations can also be represented using equations.
✔ Verification confirms the correctness of the solution.
FAQs
Q. How are three consecutive even numbers represented?
Answer:
If the smallest number is $$x$$, the three consecutive even numbers are:
$$x,\ x+2,\ x+4$$
Q. What is the perimeter of a rectangle?
Answer:
The perimeter of a rectangle is:
$$P=2(l+b)$$
Q. How do we represent twice a number plus 80?
Answer:
If the number is $$x$$, then twice the number plus 80 is:
$$2x+80$$
Q. How do we solve $$\frac{x}{6}+4=9$$?
Answer:
Subtract $$4$$:
$$\frac{x}{6}=5$$
Multiply by $$6$$:
$$x=30$$
Q. Why is verification important?
Answer:
Verification confirms that the obtained value satisfies the original equation and the conditions given in the question.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh and challenging practice on equations involving variables on both sides, fractional equations, consecutive even numbers, rectangle perimeter, and money-based applications.
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