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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: 12
Difficulty Level: Difficult
Based On: NCERT Syllabus
Introduction
A simple equation contains an unknown quantity represented by a variable. By performing the same operation on both sides of an equation, we can maintain equality and determine the unknown value.
For example:
$$6x+5=35$$
Subtracting $5$ from both sides gives:
$$6x=30$$
Therefore:
$$x=5$$
Simple equations are also useful for solving problems involving numbers, ages, money, lengths, and geometrical measurements.
This Practice Set 12 contains 5 fresh MCQs covering different applications of simple equations.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations containing fractions
✔ Finding unknown numbers
✔ Working with consecutive numbers
✔ Solving age-based problems
✔ Applying equations to geometry
✔ Verifying solutions
Why This Topic Is Important
Simple equations develop algebraic thinking and help students understand how unknown quantities can be represented mathematically.
They are also an important foundation for solving word problems and learning more advanced algebra 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:
$$11x-9=7x+19$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
B) $$7$$
Useful Concept
When the variable occurs on both sides, bring the variable terms together and then isolate the variable.
Solution
Given:
$$11x-9=7x+19$$
Subtract $$7x$$ from both sides:
$$11x-7x-9=19$$
$$4x-9=19$$
Add $$9$$:
$$4x=28$$
Divide by $$4$$:
$$x=7$$
Verification
Left side:
$$11(7)-9=77-9=68$$
Right side:
$$7(7)+19=49+19=68$$
Therefore:
$$68=68$$
Hence, the solution is correct.
Correct Answer: B) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{5}+7=13$$
A) $$20$$
B) $$25$$
C) $$30$$
D) $$35$$
Answer:
C) $$30$$
Useful Concept
First isolate the term containing the fraction and then multiply by the denominator.
Solution
Given:
$$\frac{x}{5}+7=13$$
Subtract $$7$$ from both sides:
$$\frac{x}{5}=6$$
Multiply both sides by $$5$$:
$$x=30$$
Verification
$$\frac{30}{5}+7=6+7=13$$
Therefore, the solution is correct.
Correct Answer: C) $$30$$
Q3. The sum of two consecutive even numbers is 74. What is the smaller number?
A) $$34$$
B) $$35$$
C) $$36$$
D) $$38$$
Answer:
C) $$36$$
Useful Concept
Two consecutive even numbers differ by $$2$$.
If the smaller number is $$x$$, the larger number is:
$$x+2$$
Solution
Let the smaller even number be:
$$x$$
The larger even number is:
$$x+2$$
Their sum is $$74$$:
$$x+(x+2)=74$$
Simplify:
$$2x+2=74$$
Subtract $$2$$:
$$2x=72$$
Divide by $$2$$:
$$x=36$$
Therefore, the smaller number is:
$$36$$
Verification
The two numbers are:
$$36,\ 38$$
Their sum:
$$36+38=74$$
Hence, the answer is correct.
Correct Answer: C) $$36$$
Q4. A father is 8 years more than twice his son’s age. If the father is 38 years old, what is the son’s age?
A) $$12$$ years
B) $$14$$ years
C) $$15$$ years
D) $$16$$ years
Answer:
B) $$15$$ years
Useful Concept
If the son’s age is $$x$$, twice his age is $$2x$$. Eight years more than this is:
$$2x+8$$
Solution
Let the son’s age be:
$$x$$
Father’s age:
$$2x+8$$
Given:
$$2x+8=38$$
Subtract $$8$$:
$$2x=30$$
Divide by $$2$$:
$$x=15$$
Therefore, the son’s age is:
$$15\text{ years}$$
Verification
$$2(15)+8=30+8=38$$
Therefore, the answer is correct.
Correct Answer: C) $$15$$ years
Correction: The calculated answer is $$15$$ years, which corresponds to option C, not B.
Hence, the correct answer is:
C) $$15$$ years
Q5. The length of a rectangle is 4 cm more than its breadth. If its perimeter is 56 cm, what is its length?
A) $$12$$ cm
B) $$14$$ cm
C) $$16$$ cm
D) $$18$$ cm
Answer:
C) $$16$$ cm
Useful Concept
The perimeter of a rectangle is:
$$P=2(l+b)$$
If the breadth is $$x$$, the length is $$x+4$$.
Solution
Let the breadth be:
$$x\text{ cm}$$
Then the length is:
$$x+4\text{ cm}$$
Given:
$$P=56\text{ cm}$$
Therefore:
$$2[(x+4)+x]=56$$
Simplify:
$$2(2x+4)=56$$
$$4x+8=56$$
Subtract $$8$$:
$$4x=48$$
Divide by $$4$$:
$$x=12$$
Thus, breadth is:
$$12\text{ cm}$$
Length:
$$12+4=16\text{ cm}$$
Verification
$$2(16+12)=2(28)=56\text{ cm}$$
Therefore, the length is:
$$16\text{ cm}$$
Correct Answer: C) $$16$$ cm
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:
$$\frac{x}{a}=c-b$$
Therefore:
$$x=a(c-b)$$
Two Consecutive Even Numbers
If the smaller even number is $$x$$:
$$x,\ x+2$$
Age Relationship
Twice a number:
$$2x$$
Eight more than twice a number:
$$2x+8$$
Rectangle Perimeter
$$P=2(l+b)$$
Verification
Substitute the obtained value into the original equation or condition to check the answer.
Related Practice Questions
Q1. Solve:
$$12x-8=8x+24$$
Q2. Find $$x$$:
$$\frac{x}{6}+5=12$$
Q3. The sum of two consecutive even numbers is 86. Find the numbers.
Q4. A father is 7 years more than twice his son’s age. If the father is 39 years old, find the son’s age.
Q5. A rectangle has perimeter 72 cm. Its length is 6 cm more than its breadth. Find its dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$9x-5=6x+16$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Q2. Find $$x$4:
$$\frac{x}{4}+5=12$$
A) $$24$$
B) $$28$$
C) $$32$$
D) $$36$$
Q3. Two consecutive even numbers have a sum of 82. The smaller number is:
A) $$38$$
B) $$40$$
C) $$41$$
D) $$42$$
Q4. A father is 6 years more than twice his son’s age. If the father is 36 years old, the son’s age is:
A) $$12$$
B) $$13$$
C) $$14$$
D) $$15$$
Q5. A rectangle has perimeter 60 cm. Its length is 4 cm more than its breadth. The length is:
A) $$14$$ cm
B) $$15$$ cm
C) $$16$$ cm
D) $$17$$ cm
Exam Tips
✔ Move variable terms carefully when they occur on both sides.
✔ Isolate fractional terms before multiplying.
✔ Consecutive even numbers differ by $$2$$.
✔ Define the unknown quantity before forming an equation.
✔ Translate age relationships carefully.
✔ Use the rectangle perimeter formula correctly.
✔ Always verify the final answer.
Quick Revision Notes
✔ General equation:
$$ax+b=cx+d$$
✔ Fraction:
$$\frac{x}{a}+b=c$$
✔ Consecutive even numbers:
$$x,\ x+2$$
✔ Twice a number:
$$2x$$
✔ Eight more than twice a number:
$$2x+8$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive even numbers as numbers differing by $$1$$.
❌ Forgetting to multiply by the denominator after isolating a fraction.
❌ Confusing “8 more than twice” with “8 times”.
❌ Using the wrong rectangle perimeter formula.
❌ Making sign errors while shifting terms.
❌ Not checking the final answer.
Key Takeaways
✔ Simple equations help find unknown quantities.
✔ Variables may appear on both sides of an equation.
✔ Fractions can be solved using inverse operations.
✔ Consecutive even numbers differ by $$2$$.
✔ Age relationships can be expressed using variables.
✔ Geometry problems can be converted into equations.
✔ Verification ensures that the obtained answer is correct.
FAQs
Q. How are two consecutive even numbers represented?
Answer:
If the smaller even number is $$x$$, the two numbers are:
$$x,\ x+2$$
Q. How do we represent twice a number plus 8?
Answer:
If the number is $$x$$, twice the number plus 8 is:
$$2x+8$$
Q. What is the perimeter formula for a rectangle?
Answer:
The perimeter is:
$$P=2(l+b)$$
Q. How do we solve $$\frac{x}{5}+7=13$$?
Answer:
Subtract $$7$$:
$$\frac{x}{5}=6$$
Then multiply by $$5$$:
$$x=30$$
Q. Why should an equation be verified?
Answer:
Verification confirms that the obtained value satisfies the original equation.
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, fractions, consecutive even numbers, age problems, and rectangle-based applications.
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