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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, 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: 10
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
Simple equations help us find unknown quantities by expressing mathematical relationships using variables. An equation remains balanced when the same operation is performed on both sides.
For example:
$$4x+9=25$$
Subtracting $$9$$ from both sides gives:
$$4x=16$$
and therefore:
$$x=4$$
Simple equations can also be used to solve practical problems involving ages, numbers, costs, lengths, and other quantities.
This Practice Set 10 contains 5 fresh MCQs designed to improve algebraic reasoning and problem-solving skills.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Forming equations from statements
✔ Solving consecutive-number problems
✔ Applying equations to geometry and daily-life situations
✔ Verifying solutions
Why This Topic Is Important
Simple equations are an essential foundation of algebra. They teach students how to convert information into mathematical equations and systematically find unknown values.
The ability to solve equations is also useful in geometry, word problems, and higher-level mathematics.
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:
$$7x+5=4x+26$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
B) $$7$$
Useful Concept
When a variable appears on both sides, collect the variable terms on one side and constants on the other.
Solution
Given:
$$7x+5=4x+26$$
Subtract $$4x$$ from both sides:
$$7x-4x+5=26$$
$$3x+5=26$$
Subtract $$5$$ from both sides:
$$3x=21$$
Divide by $$3$$:
$$x=7$$
Verification
Left side:
$$7(7)+5=49+5=54$$
Right side:
$$4(7)+26=28+26=54$$
Therefore:
$$54=54$$
Hence, the solution is correct.
Correct Answer: B) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{8}-3=5$$
A) $$48$$
B) $$56$$
C) $$64$$
D) $$72$$
Answer:
C) $$64$$
Useful Concept
First isolate the fractional term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{8}-3=5$$
Add $$3$$ to both sides:
$$\frac{x}{8}=8$$
Multiply both sides by $$8$$:
$$x=64$$
Verification
$$\frac{64}{8}-3=8-3=5$$
Therefore, the solution is correct.
Correct Answer: C) $$64$$
Q3. The sum of three consecutive odd numbers is 81. What is the largest number?
A) $$25$$
B) $$27$$
C) $$29$$
D) $$31$$
Answer:
C) $$29$$
Useful Concept
Three consecutive odd numbers differ by $$2$$. If the smallest is $$x$$, they can be represented as:
$$x,\ x+2,\ x+4$$
Solution
Let the smallest odd number be:
$$x$$
The three numbers are:
$$x,\quad x+2,\quad x+4$$
Their sum is $$81$$:
$$x+(x+2)+(x+4)=81$$
Simplify:
$$3x+6=81$$
Subtract $$6$$:
$$3x=75$$
Divide by $$3$$:
$$x=25$$
Therefore, the three numbers are:
$$25,\ 27,\ 29$$
Hence, the largest number is:
$$29$$
Verification
$$25+27+29=81$$
Therefore, the answer is correct.
Correct Answer: C) $$29$$
Q4. A mother’s age is 5 years more than twice her daughter’s age. If the mother is 35 years old, what is the daughter’s age?
A) $$12$$ years
B) $$13$$ years
C) $$14$$ years
D) $$15$$ years
Answer:
C) $$15$$ years
Useful Concept
If the daughter’s age is $$x$$, twice her age is $$2x$$. Five years more than this is:
$$2x+5$$
Solution
Let the daughter’s age be:
$$x$$
Mother’s age:
$$2x+5$$
Given:
$$2x+5=35$$
Subtract $$5$$:
$$2x=30$$
Divide by $$2$$:
$$x=15$$
Therefore, the daughter’s age is:
$$15\text{ years}$$
Verification
$$2(15)+5=30+5=35$$
Hence, the answer is correct.
Correct Answer: D) $$15$$ years
Correction: The calculated answer is $$15$$ years, which corresponds to option D, not C.
Therefore, the correct answer is:
D) $$15$$ years
Q5. The perimeter of a square is 68 cm. What is the length of each side?
A) $$15$$ cm
B) $$16$$ cm
C) $$17$$ cm
D) $$18$$ cm
Answer:
C) $$17$$ cm
Useful Concept
A square has four equal sides.
Therefore:
$$P=4s$$
where $$s$$ represents the side length.
Solution
Given:
$$P=68\text{ cm}$$
Let the side be:
$$x\text{ cm}$$
Then:
$$4x=68$$
Divide both sides by $$4$$:
$$x=17$$
Therefore, each side of the square is:
$$17\text{ cm}$$
Verification
$$4(17)=68\text{ cm}$$
Hence, the answer is correct.
Correct Answer: C) $$17$$ cm
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:
$$\frac{x}{a}=b+c$$
and therefore:
$$x=a(b+c)$$
Three Consecutive Odd Numbers
If the smallest number is $$x$$:
$$x,\ x+2,\ x+4$$
Square Perimeter
For a square:
$$P=4s$$
where $$s$$ is the side length.
Twice a Number
$$2x$$
Five More Than Twice a Number
$$2x+5$$
Verification
Substitute the obtained value into the original equation to confirm the result.
Related Practice Questions
Q1. Solve:
$$8x+3=5x+24$$
Q2. Find $x$:
$$\frac{x}{7}-2=6$$
Q3. The sum of three consecutive odd numbers is 99. Find the largest number.
Q4. A father’s age is 4 years more than twice his son’s age. If the father is 40 years old, find the son’s age.
Q5. The perimeter of a square is 84 cm. Find the length of each side.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$9x-4=5x+20$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Find $$x$$:
$$\frac{x}{6}+2=9$$
A) $$36$$
B) $$42$$
C) $$48$$
D) $$54$$
Q3. Three consecutive odd numbers have a sum of 87. The largest number is:
A) $$27$$
B) $$29$$
C) $$31$$
D) $$33$$
Q4. A mother is 6 years more than twice her daughter’s age. If the mother is 34 years old, the daughter’s age is:
A) $$12$$
B) $$13$$
C) $$14$$
D) $$15$$
Q5. The perimeter of a square is 76 cm. Its side is:
A) $$17$$ cm
B) $$18$$ cm
C) $$19$$ cm
D) $$20$$ cm
Exam Tips
✔ When variables appear on both sides, collect them carefully.
✔ Isolate the fractional term before multiplying by the denominator.
✔ Remember that consecutive odd numbers differ by $$2$$.
✔ For three consecutive odd numbers, use:
$$x,\ x+2,\ x+4$$
✔ Remember the square perimeter formula:
$$P=4s$$
✔ Translate age relationships carefully.
✔ Always verify the final answer.
Quick Revision Notes
✔ Variable on both sides:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}-b=c$$
✔ Three consecutive odd numbers:
$$x,\ x+2,\ x+4$$
✔ Square perimeter:
$$P=4s$$
✔ Twice a number:
$$2x$$
✔ Five more than twice a number:
$$2x+5$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive odd numbers as numbers differing by $$1$$.
❌ Forgetting to add the constant before removing a fraction.
❌ Using $P=2s$ for a square instead of $$P=4s$$.
❌ Confusing “twice a number” with “the number plus 2”.
❌ Making sign errors while shifting terms.
❌ Not verifying the answer.
Key Takeaways
✔ Simple equations help determine unknown quantities.
✔ Variables can occur on both sides of an equation.
✔ Fractions can be handled using inverse operations.
✔ Consecutive odd numbers differ by $$2$$.
✔ Age problems can be represented using variables.
✔ Square perimeter problems can be solved using equations.
✔ Verification confirms the correctness of a solution.
FAQs
Q. How are three consecutive odd numbers represented?
Answer:
If the smallest odd number is $$x$$, the three consecutive odd numbers are:
$$x,\ x+2,\ x+4$$
Q. What is the perimeter of a square?
Answer:
The perimeter of a square is:
$$P=4s$$
where $$s$$ is the length of one side.
Q. How do we represent five more than twice a number?
Answer:
If the number is $x$, twice the number is $$2x$$. Five more than it is:
$$2x+5$$
Q. How do we solve $$\frac{x}{8}-3=5$$?
Answer:
Add $$3$$:
$$\frac{x}{8}=8$$
Then multiply by $$8$$:
$$x=64$$
Q. Why is verification necessary?
Answer:
Verification checks whether the obtained value actually satisfies the original equation.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on equations with variables on both sides, fractional equations, consecutive odd numbers, age-based problems, and square perimeter applications.
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