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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, number relationships, consecutive integers, 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: 8
Difficulty Level: Moderate to Difficult
Based On: NCERT Syllabus
Introduction
Simple equations allow us to represent unknown quantities and solve problems using mathematical relationships. In many situations, an unknown quantity may be related to another quantity through multiplication, addition, subtraction, or division.
For example:
$$3x-4=20$$
To solve such an equation, we use inverse operations while keeping both sides of the equation balanced.
In Practice Set 8, students will practise fresh MCQs involving equations with variables on both sides, fractional relationships, consecutive numbers, ages, and real-life applications.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Forming equations from word statements
✔ Working with consecutive numbers
✔ Solving age and money-based problems
✔ Verifying solutions
Why This Topic Is Important
Simple equations are essential for developing algebraic reasoning. They help students convert verbal information into mathematical expressions and equations and then find unknown quantities systematically.
These skills are useful in school examinations as well as in later algebraic topics.
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:
$$8x-9=5x+12$$
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.
Solution
Given:
$$8x-9=5x+12$$
Subtract $$5x$$ from both sides:
$$8x-5x-9=12$$
$$3x-9=12$$
Add $$9$$ to both sides:
$$3x=21$$
Divide by $$3$$:
$$x=7$$
Verification
Left side:
$$8(7)-9=56-9=47$$
Right side:
$$5(7)+12=35+12=47$$
Since both sides are equal:
$$47=47$$
Therefore, the solution is correct.
Hence, the correct answer is:
C) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{5}-2=6$$
A) $$30$$
B) $$35$$
C) $$40$$
D) $$45$$
Answer:
C) $$40$$
Useful Concept
First remove the constant term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{5}-2=6$$
Add $$2$$ to both sides:
$$\frac{x}{5}=8$$
Multiply both sides by $$5$$:
$$x=40$$
Verification
$$\frac{40}{5}-2=8-2=6$$
Therefore, the solution is correct.
Hence, the correct answer is:
C) $$40$$
Q3. The sum of two consecutive odd numbers is 64. What is the smaller number?
A) $$29$$
B) $$31$$
C) $$33$$
D) $$35$$
Answer:
B) $$31$$
Useful Concept
Two consecutive odd numbers differ by $$2$$. If the smaller number is $$x$$, the next odd number is $$x+2$$.
Solution
Let the smaller odd number be:
$$x$$
The next consecutive odd number is:
$$x+2$$
Their sum is $$64$$:
$$x+(x+2)=64$$
Simplify:
$$2x+2=64$$
Subtract $$2$$:
$$2x=62$$
Divide by $$2$$:
$$x=31$$
Therefore, the smaller number is:
$$31$$
Verification
The two numbers are:
$$31,\ 33$$
Their sum:
$$31+33=64$$
Hence, the answer is correct.
Correct Answer: B) $$31$$
Q4. A number is 8 less than three times another number. If the larger number is 28, what is the smaller number?
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Answer:
C) $$12$$
Useful Concept
“Three times a number” means $$3x$$, and “8 less than” means subtracting $$8$$.
Solution
Let the smaller number be:
$$x$$
The larger number is 8 less than three times the smaller number:
$$3x-8$$
Given that the larger number is $$28$$:
$$3x-8=28$$
Add $$8$$:
$$3x=36$$
Divide by $$34$:
$$x=12$$
Therefore, the smaller number is:
$$12$$
Verification
$$3(12)-8=36-8=28$$
Therefore, the answer is correct.
Hence, the correct answer is:
C) $$12$$
Q5. A father is 4 years more than three times his son’s age. If the father is 40 years old, what is the son’s age?
A) $$10$$ years
B) $$11$$ years
C) $$12$$ years
D) $$13$$ years
Answer:
B) $$12$$ years
Useful Concept
If the son’s age is $$x$$, three times his age is $$3x$$. Four years more than this is:
$$3x+4$$
Solution
Let the son’s age be:
$$x$$
Father’s age:
$$3x+4$$
Given father’s age is $$40$$:
$$3x+4=40$$
Subtract $$4$$:
$$3x=36$$
Divide by $$3$$:
$$x=12$$
Therefore, the son’s age is:
$$12\text{ years}$$
Verification
$$3(12)+4=36+4=40$$
Therefore, the answer is correct.
Correction: The calculated value is $$12$$ years, which corresponds to option C, not B.
Hence, the correct answer is:
C) $$12$$ years
Important Formulas & Concepts
Variable on Both Sides
For:
$$ax+b=cx+d$$
collect variable terms on one side and constants on the other.
Fractional Equation
For:
$$\frac{x}{a}-b=c$$
add $$b$$ first:
$$\frac{x}{a}=b+c$$
then:
$$x=a(b+c)$$
Consecutive Odd Numbers
If the smaller odd number is $$x$$:
$$x,\ x+2$$
Consecutive Even Numbers
If the smaller even number is $$x$$:
$$x,\ x+2$$
Three Times a Number
$$3x$$
More Than
“4 more than $$3x$$”:
$$3x+4$$
Less Than
“8 less than $$3x$$”:
$$3x-8$$
Verification
Always substitute the obtained value into the original equation.
Related Practice Questions
Q1. Solve:
$$7x-5=4x+16$$
Q2. Find $$x$$:
$$\frac{x}{6}-3=5$$
Q3. The sum of two consecutive odd numbers is 76. Find the numbers.
Q4. A number is 5 less than twice another number. If the larger number is 21, find the smaller number.
Q5. A father is 6 years more than twice his son’s age. If the father is 36 years old, find the son’s age.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$6x-4=3x+17$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$$:
$$\frac{x}{4}-3=5$$
A) $$24$$
B) $$28$$
C) $$32$$
D) $$36$$
Q3. Two consecutive odd numbers have a sum of 72. The smaller number is:
A) $$33$$
B) $$34$$
C) $$35$$
D) $$37$$
Q4. A number is 6 less than twice another number. If the larger number is 18, the smaller number is:
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Q5. A father is 5 years more than twice his son’s age. If the father is 35 years old, the son’s age is:
A) $$12$$
B) $$15$$
C) $$18$$
D) $$20$$
Exam Tips
✔ Collect variable terms carefully when they occur on both sides.
✔ For fractional equations, first isolate the fractional term.
✔ Consecutive odd or even numbers differ by $$2$$.
✔ Carefully distinguish between “more than” and “less than”.
✔ Define the variable before forming an equation.
✔ Check age and money calculations carefully.
✔ Verify the final answer using the original equation.
Quick Revision Notes
✔ Variable on both sides:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}=b\Rightarrow x=ab$$
✔ Consecutive odd numbers:
$$x,\ x+2$$
✔ Consecutive even numbers:
$$x,\ x+2$$
✔ Three times a number:
$$3x$$
✔ Four more than $$3x$$:
$$3x+4$$
✔ Eight less than $$3x$$:
$$3x-8$$
✔ Verification confirms the solution.
Common Mistakes Students Make
❌ Treating consecutive odd numbers as numbers differing by $$1$$.
❌ Forgetting to add a constant before removing a fraction.
❌ Confusing “8 less than” with “8 more than”.
❌ Writing the wrong expression for “three times a number”.
❌ Making errors when moving variable terms.
❌ Not checking the answer against the original problem.
Key Takeaways
✔ Equations can represent relationships between unknown quantities.
✔ Variables may appear on both sides of an equation.
✔ Fractions can be solved using inverse operations.
✔ Consecutive odd and even numbers differ by $$2$$.
✔ Age relationships can be represented using equations.
✔ Verification helps ensure the solution is correct.
FAQs
Q. What are consecutive odd numbers?
Answer:
Consecutive odd numbers are odd numbers that differ by $$2$$.
For example:
$$21,\ 23,\ 25$$
Q. How do we solve $$\frac{x}{5}-2=6$$?
Answer:
Add $$2$$ to both sides:
$$\frac{x}{5}=8$$
Then multiply by $$5$$:
$$x=40$$
Q. What does “8 less than three times a number” mean?
Answer:
If the number is $$x$$, three times the number is $$3x$$, and 8 less than it is:
$$3x-8$$
Q. What does “4 more than three times a number” mean?
Answer:
It means:
$$3x+4$$
Q. Why should we verify an answer?
Answer:
Verification ensures that the value obtained satisfies the original equation and the conditions of the problem.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on equations involving variables on both sides, fractions, consecutive odd numbers, number relationships, and age-based applications.
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