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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: 15
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 equal values.
For example:
$$5x+9=34$$
Subtracting $$9$$ from both sides:
$$5x=25$$
Therefore:
$$x=5$$
Simple equations are useful for solving problems involving unknown numbers, ages, money, distances, lengths, and geometrical measurements.
This Practice Set 15 is the final set of this series and 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 odd numbers
✔ Translating verbal statements into equations
✔ Solving age-related problems
✔ Applying equations to geometry
✔ Verifying solutions
Why This Topic Is Important
Simple equations provide students with an important foundation in algebra. They teach students how to represent unknown quantities using variables and solve problems systematically.
These skills are useful for mathematical reasoning, word problems, geometry, and algebraic concepts 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:
$$15x-17=10x+23$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
C) $$8$$
Useful Concept
When the variable occurs on both sides, collect all variable terms on one side and constants on the other.
Solution
Given:
$$15x-17=10x+23$$
Subtract $$10x$$ from both sides:
$$15x-10x-17=23$$
$$5x-17=23$$
Add $$17$$ to both sides:
$$5x=40$$
Divide by $$5$$:
$$x=8$$
Verification
Left side:
$$15(8)-17=120-17=103$$
Right side:
$$10(8)+23=80+23=103$$
Therefore:
$$103=103$$
Hence, the solution is correct.
Correct Answer: C) $$8$$
Q2. Find the value of $$x$$:
$$\frac{x}{6}-5=4$$
A) $$42$$
B) $$48$$
C) $$54$$
D) $$60$$
Answer:
C) $$54$$
Useful Concept
First isolate the fractional term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{6}-5=4$$
Add $$5$$ to both sides:
$$\frac{x}{6}=9$$
Multiply both sides by $$6$$:
$$x=54$$
Verification
$$\frac{54}{6}-5=9-5=4$$
Therefore, the solution is correct.
Correct Answer: C) $$54$$
Q3. The sum of three consecutive even numbers is 102. What is the largest number?
A) $$32$$
B) $$34$$
C) $$36$$
D) $$38$$
Answer:
C) $$36$$
Useful Concept
Three consecutive even numbers differ by $$2$$ and can be represented as:
$$x,\ x+2,\ x+4$$
Solution
Let the smallest even number be:
$$x$$
Then the three numbers are:
$$x,\quad x+2,\quad x+4$$
Their sum is $$102$$:
$$x+(x+2)+(x+4)=102$$
Simplify:
$$3x+6=102$$
Subtract $$6$$:
$$3x=96$$
Divide by $$3$$:
$$x=32$$
Therefore, the three numbers are:
$$32,\ 34,\ 36$$
The largest number is:
$$36$$
Verification
$$32+34+36=102$$
Hence, the answer is correct.
Correct Answer: C) $$36$$
Q4. A mother 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) $$15$$ years
D) $$16$$ years
Answer:
C) $$15$$ years
Useful Concept
If the daughter’s age is $$x$$, twice her age is $$2x$$. Five years more than twice her age 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: C) $$15$$ years
Q5. The perimeter of a rectangular park is 96 m. Its length is 8 m more than its breadth. What is the length of the park?
A) $$24$$ m
B) $$26$$ m
C) $$28$$ m
D) $$30$$ m
Answer:
C) $$28$$ m
Useful Concept
The perimeter of a rectangle is:
$$P=2(l+b)$$
If the breadth is $$x$$, the length is:
$$x+8$$
Solution
Let the breadth be:
$$x\text{ m}$$
Then the length is:
$$x+8\text{ m}$$
Given:
$$P=96\text{ m}$$
Therefore:
$$2[(x+8)+x]=96$$
Simplify:
$$2(2x+8)=96$$
$$4x+16=96$$
Subtract $$16$$:
$$4x=80$$
Divide by $$4$$:
$$x=20$$
Therefore, breadth is:
$$20\text{ m}$$
Length:
$$20+8=28\text{ m}$$
Verification
$$2(28+20)=2(48)=96\text{ m}$$
Therefore, the length is:
$$28\text{ m}$$
Correct Answer: C) $$28$$ 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:
$$\frac{x}{a}=b+c$$
Therefore:
$$x=a(b+c)$$
Three Consecutive Even Numbers
If the smallest number is $$x$$:
$$x,\ x+2,\ x+4$$
Twice a Number Plus 5
$$2x+5$$
Rectangle Perimeter
$$P=2(l+b)$$
Verification
Substitute the obtained value into the original equation or condition to check whether it satisfies the given problem.
Related Practice Questions
Q1. Solve:
$$16x-13=11x+27$$
Q2. Find $$x$$:
$$\frac{x}{7}-4=5$$
Q3. The sum of three consecutive even numbers is 126. Find the largest number.
Q4. A father is 4 years more than twice his son’s age. If the father is 36 years old, find the son’s age.
Q5. A rectangular field has a perimeter of 104 m. Its length is 10 m more than its breadth. Find its dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$14x-9=9x+26$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$$:
$$\frac{x}{8}-3=5$$
A) $$48$$
B) $$56$$
C) $$64$$
D) $$72$$
Q3. Three consecutive even numbers have a sum of 114. The largest number is:
A) $$36$$
B) $$38$$
C) $$40$$
D) $$42$$
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. A rectangle has perimeter 88 cm. Its length is 6 cm more than its breadth. The length is:
A) $$24$$ cm
B) $$25$$ cm
C) $$26$$ cm
D) $$27$$ cm
Exam Tips
✔ Move variable terms carefully from one side to the other.
✔ Remember to change signs correctly when transposing terms.
✔ Isolate fractional terms before multiplying by the denominator.
✔ Consecutive even numbers differ by $$2$$.
✔ Translate age relationships carefully.
✔ Use:
$$P=2(l+b)$$
for rectangle perimeter problems.
✔ Always verify the final answer.
Quick Revision Notes
✔ Equation with variables on both sides:
$$ax+b=cx+d$$
✔ Fractional equation:
$$\frac{x}{a}-b=c$$
✔ Three consecutive even numbers:
$$x,\ x+2,\ x+4$$
✔ Twice a number plus 5:
$$2x+5$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Changing the sign incorrectly while moving terms.
❌ Treating consecutive even numbers as numbers differing by $$1$$.
❌ Forgetting to multiply by the denominator.
❌ Confusing “five more than twice” with “five times”.
❌ Using an incorrect rectangle perimeter formula.
❌ Skipping verification.
Key Takeaways
✔ Simple equations can be solved systematically using inverse operations.
✔ Variables may occur on both sides of an equation.
✔ Fractions can be handled by isolating the fractional term.
✔ Consecutive even numbers differ by $$2$$.
✔ Age relationships can be expressed using variables.
✔ Rectangle problems can be converted into simple equations.
✔ Verification confirms the correctness of a solution.
FAQs
Q. What is a simple equation?
Answer:
A simple equation is a mathematical statement containing an unknown quantity represented by a variable and an equality sign.
For example:
$$3x+4=19$$
Q. How are three consecutive even numbers represented?
Answer:
If the smallest even number is $$x$$, the three numbers are:
$$x,\ x+2,\ x+4$$
Q. What does “5 more than twice a number” mean?
Answer:
If the number is $$x$$, the expression is:
$$2x+5$$
Q. What is the perimeter of a rectangle?
Answer:
The perimeter is:
$$P=2(l+b)$$
where $l$ is the length and $$b$$ is the breadth.
Q. Why is verification important?
Answer:
Verification checks whether the value obtained actually satisfies the original equation or condition.
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 even numbers, age-based problems, and rectangle-based applications.
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