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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 solving equations, forming equations from statements, verification, and application-based problems.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 4
Difficulty Level: Moderate
Based On: NCERT Syllabus
Introduction
A simple equation is a mathematical statement that contains an equality sign and an unknown quantity. We can find the unknown by applying suitable operations to both sides of the equation.
For example:
$$2x+7=21$$
To solve this equation, we first remove the constant term and then determine the value of the variable.
In Practice Set 4, students will practise equations with different operations, number-based statements, and simple application-based questions.
What You Will Learn
✔ Solving equations with multiple operations
✔ Translating statements into equations
✔ Finding unknown numbers
✔ Using inverse operations
✔ Verifying solutions
✔ Applying equations to practical situations
Why This Topic Is Important
Simple equations help students understand how unknown quantities can be represented and calculated mathematically. They also develop logical thinking and prepare students for algebraic equations studied 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:
$$5x+3=28$$
A) $$4$$
B) $$5$$
C) $$6$$
D) $$7$4
Answer:
B) $$5$$
Useful Concept
When an equation contains a variable term and a constant, first remove the constant using the inverse operation.
Solution
Given:
$$5x+3=28$$
Subtract $3$ from both sides:
$$5x+3-3=28-3$$
$$5x=25$$
Now divide both sides by $$5$$:
$$x=\frac{25}{5}$$
Therefore:
$$x=5$$
Verification
Substitute $$x=5$$:
$$5(5)+3=25+3=28$$
$$28=28$$
Therefore, the solution is correct.
Hence, the correct answer is:
B) $$5$$
Q2. If
$$7x-6=36,$$
then the value of $$x$$ is:
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer:
B) $$6$$
Useful Concept
When a number is subtracted from a variable term, add the same number to both sides before dividing by the coefficient.
Solution
Given:
$$7x-6=36$$
Add $6$ to both sides:
$$7x-6+6=36+6$$
$$7x=42$$
Divide both sides by $$7$$:
$$x=\frac{42}{7}$$
Therefore:
$$x=6$$
Verification
$$7(6)-6=42-6=36$$
Thus, the answer is correct.
Hence, the correct answer is:
B) $$6$$
Q3. Which equation represents the statement:
“Three times a number is 18 more than the number”?
A) $$3x=18$$
B) $$3x=x+18$$
C) $$3x=x-18$$
D) $$3+x=18$$
Answer:
B) $$3x=x+18$$
Useful Concept
“Three times a number” means $$3x$$, while “18 more than the number” means $$x+18$$.
Solution
Let the number be:
$$x$$
Three times the number:
$$3x$$
18 more than the number:
$$x+18$$
Therefore:
$$3x=x+18$$
Hence, the correct answer is:
B) $$3x=x+18$$
We can also solve the equation:
$$3x=x+18$$
Subtract $$x$$ from both sides:
$$3x-x=18$$
$$2x=18$$
Therefore:
$$x=9$$
Verification:
$$3(9)=27$$
and:
$$9+18=27$$
Thus, both sides are equal.
Q4. The sum of two consecutive numbers is 31. If the smaller number is $$x$$, which equation represents the situation?
A) $$x+x=31$$
B) $$x+(x+1)=31$$
C) $$x+(x+2)=31$$
D) $$2x+2=31$$
Answer:
B) $$x+(x+1)=31$$
Useful Concept
Two consecutive numbers differ by $$1$$. If the smaller number is $$x$$, the next number is:
$$x+1$$
Solution
Let the smaller number be:
$$x$$
Then the consecutive number is:
$$x+1$$
Their sum is $$31$$:
$$x+(x+1)=31$$
Therefore, the required equation is:
B) $$x+(x+1)=31$$
Simplifying:
$$2x+1=31$$
Subtract $1$:
$$2x=30$$
Divide by $$2$$:
$$x=15$$
Therefore, the two consecutive numbers are:
$$15\text{ and }16$$
Verification:
$$15+16=31$$
Hence, the equation is correct.
Q5. A mother is 5 years older than twice her daughter’s age. If the mother is 29 years old and the daughter’s age is $$x$$ years, which equation represents the situation?
A) $$2x-5=29$$
B) $$2x+5=29$$
C) $$x+5=29$$
D) $$5x+2=29$$
Answer:
B) $$2x+5=29$$
Useful Concept
“Twice the daughter’s age” means $$2x$$. Five years older means adding $$5$$.
Solution
Let the daughter’s age be:
$$x$$
Twice her age:
$$2x$$
The mother is 5 years older than twice her daughter’s age:
$$2x+5$$
The mother’s age is $$29$$:
$$2x+5=29$$
Therefore, the required equation is:
B) $$2x+5=29$$
Solving:
$$2x+5=29$$
Subtract $$5$$:
$$2x=24$$
Divide by $$2$$:
$$x=12$$
Thus, the daughter’s age is $$12$$ years.
Verification:
$$2(12)+5=24+5=29$$
Therefore, the equation is correct.
Important Formulas & Concepts
Equation with Addition
For:
$$ax+b=c$$
we get:
$$ax=c-b$$
and:
$$x=\frac{c-b}{a}$$
Equation with Subtraction
For:
$$ax-b=c$$
we get:
$$ax=c+b$$
and:
$$x=\frac{c+b}{a}$$
Consecutive Numbers
If the first number is $$x$$, the next consecutive number is:
$$x+1$$
The third consecutive number is:
$$x+2$$
Twice a Number
Twice a number $$x$$ is:
$$2x$$
Three Times a Number
Three times a number$$x$$ is:
$$3x$$
More Than
“5 more than $$x$$” means:
$$x+5$$
Less Than
“5 less than $$x$$” means:
$$x-5$$
Verification
Substitute the obtained value into the original equation and check whether both sides are equal.
Related Practice Questions
Q1. Solve:
$$4x+5=25$$
Q2. Solve:
$$6x-8=28$$
Q3. Write an equation for:
Four times a number is 12 more than the number.
Q4. The sum of two consecutive numbers is 45. Find the numbers.
Q5. A number is twice another number plus 6. If the first number is 20, form an equation and find the second number.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$4x+3=19$$
A) $$3$$
B) $$4$$
C) $5$$
D) $$6$$
Q2. Solve:
$$5x-10=25$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q3. Which equation represents “twice a number plus 4 is 18”?
A) $$2x-4=18$$
B) $$2x+4=18$$
C) $$x+2+4=18$$
D) $$4x+2=18$$
Q4. If the smaller of two consecutive numbers is $$x$$, the larger number is:
A) $$x-1$$
B) $$x+1$$
C) $$2x$$
D) $$x+2$$
Q5. Solve:
$$3x+6=24$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Exam Tips
✔ Translate verbal statements carefully into equations.
✔ Remember that consecutive numbers differ by $$1$4.
✔ “Twice” means multiplication by $$2$$.
✔ “Three times” means multiplication by $$3$$.
✔ “More than” generally indicates addition.
✔ “Less than” generally indicates subtraction.
✔ Solve equations systematically and verify your answer.
✔ In age problems, clearly define the unknown age before forming the equation.
Quick Revision Notes
✔ $$ax+b=c$$:
$$x=\frac{c-b}{a}$$
✔ $$ax-b=c$$:
$$x=\frac{c+b}{a}$$
✔ Consecutive numbers:
$$x,\ x+1$$
✔ Twice a number:
$$2x$$
✔ Three times a number:
$$3x$$
✔ Five more than a number:
$$x+5$$
✔ Five less than a number:
$$x-5$$
✔ Always verify the final answer.
Common Mistakes Students Make
❌ Writing $$x-1$$ instead of $$x+1$$ for the next consecutive number.
❌ Confusing “more than” with “less than”.
❌ Forgetting the coefficient when writing twice or three times a number.
❌ Forming an equation without defining the variable.
❌ Making arithmetic errors while simplifying.
❌ Not verifying the final solution.
Key Takeaways
✔ Equations can represent relationships between unknown quantities.
✔ Verbal statements can be converted into algebraic equations.
✔ Consecutive numbers differ by $$1$$.
✔ “Twice” and “three times” indicate multiplication.
✔ Age and number problems can be solved using simple equations.
✔ Verification helps confirm the correctness of the solution.
FAQs
Q. What are consecutive numbers?
Answer:
Consecutive numbers are numbers that follow one another with a difference of $$1$$.
For example:
$$10,\ 11,\ 12$$
Q. How do we represent twice a number?
Answer:
If the number is $$x$$, twice the number is:
$$2x$$
Q. What does “5 more than a number” mean?
Answer:
If the number is $$%x$$, then 5 more than the number is:
$$x+5$$
Q. How do we represent the next consecutive number?
Answer:
If the first number is $$x$$, the next consecutive number is:
$$x+1$$
Q. Why should we define the variable in a word problem?
Answer:
Defining the variable clearly helps us translate the given information into a correct mathematical equation.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on equations involving multiple operations, consecutive numbers, age problems, and mathematical statements.
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