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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 with variables on both sides, fractions, number relationships, age problems, and verification.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 6
Difficulty Level: Moderate to Difficult
Based On: NCERT Syllabus
Introduction
Simple equations can be used to represent relationships between known and unknown quantities. As equations become more complex, the variable may appear on both sides or may be part of a fraction.
For example:
$$\frac{x}{3}+4=10$$
To solve such an equation, we use inverse operations carefully and maintain equality on both sides.
In Practice Set 6, students will practise fresh equations involving variables on both sides, fractional forms, number relationships, and application-based situations.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Translating word statements into equations
✔ Solving number-based problems
✔ Applying equations to real-life situations
✔ Verifying solutions
Why This Topic Is Important
Learning to solve different forms of equations strengthens algebraic reasoning and prepares students for more advanced mathematical concepts.
Equations involving fractions, unknown quantities, and relationships are also commonly used in school examinations and application-based questions.
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:
$$4x+7=2x+21$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$48$$
Answer:
C) $$7$$
Useful Concept
When a variable appears on both sides, collect all variable terms on one side and constants on the other.
Solution
Given:
$$4x+7=2x+21$$
Subtract $$2x$$ from both sides:
$$4x-2x+7=21$$
$$2x+7=21$$
Subtract $$7$$ from both sides:
$$2x=14$$
Divide by $$2$$:
$$x=7$$
Verification
Left side:
$$4(7)+7=28+7=35$$
Right side:
$$2(7)+21=14+21=35$$
Since both sides are equal, the solution is correct.
Hence, the correct answer is:
C) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{4}+3=8$$
A) $$16$$
B) $$18$$
C) $$20$$
D) $$22$$
Answer:
C) $$20$$
Useful Concept
First remove the constant term, then multiply by the denominator to find the variable.
Solution
Given:
$$\frac{x}{4}+3=8$$
Subtract $$3$$ from both sides:
$$\frac{x}{4}=5$$
Multiply both sides by $$4$$:
$$x=5\times4$$
Therefore:
$$x=20$$
Verification
$$\frac{20}{4}+3=5+3=8$$
Thus, the solution is correct.
Hence, the correct answer is:
C) $$20$$
Q3. The sum of a number and one-third of the same number is 24. What is the number?
A) $$15$$
B) $$18$$
C) $$20$$
D) $$21$$
Answer:
B) $$18$$
Useful Concept
If the number is $$x$$, one-third of the number is:
$$\frac{x}{3}$$
Solution
Let the number be:
$$x$$
One-third of the number:
$$\frac{x}{3}$$
According to the question:
$$x+\frac{x}{3}=24$$
Multiply the entire equation by $3$:
$$3x+x=72$$
Therefore:
$$4x=72$$
Divide by $$4$$:
$$x=18$$
Verification
$$18+\frac{18}{3}=18+6=24$$
Therefore, the answer is correct.
Hence, the correct answer is:
B) $$18$$
Correction: The calculated value is $$18$$, but in the options above, $$18$$ is option B, not C.
Therefore, the correct answer is:
B) $18$
Q4. A number is 7 more than twice another number. If the larger number is 25, what is the smaller number?
A) $$7$$
B) $$8$$
C) $$9$$
D) $$10$$
Answer:
C) $$9$$
Useful Concept
“Twice a number” means $$2x$$, and “7 more” means $$2x+7$$.
Solution
Let the smaller number be:
$$x$$
The larger number is 7 more than twice the smaller number:
$$2x+7$$
The larger number is $$25$$:
$$2x+7=25$$
Subtract $$7$$:
$$2x=18$$
Divide by $$2$$:
$$x=9$$
Therefore, the smaller number is:
$$9$$
Verification
$$2(9)+7=18+7=25$$
Hence, the answer is correct.
Q5. The perimeter of a rectangle is 50 cm. Its length is 5 cm more than its breadth. What is the breadth?
A) $$8$$ cm
B) $$9$$cm
C) $$10$$ cm
D) $$12$$ cm
Answer:
C) $$10$$ cm
Useful Concept
For a rectangle:
$$P=2(l+b)$$
If breadth is $$x$$, and length is 5 cm more, then:
$$l=x+5$$
Solution
Let the breadth be:
$$x\text{ cm}$$
Then the length is:
$$x+5\text{ cm}$$
The perimeter is:
$$50\text{ cm}$$
Using:
$$P=2(l+b)$$
we get:
$$2[(x+5)+x]=50$$
Simplify:
$$2(2x+5)=50$$
$$4x+10=50$$
Subtract $$10$$:
$$4x=40$$
Divide by $$4$$:
$$x=10$$
Therefore, the breadth is:
$$10\text{ cm}$$
Verification
Length:
$$10+5=15\text{ cm}$$
Perimeter:
$$2(15+10)=2(25)=50\text{ cm}$$
Thus, the answer is correct.
Hence, the correct answer is:
C) $$10$$ cm
Important Formulas & Concepts
Fractional Equation
For:
$$\frac{x}{a}=b$$
we get:
$$x=ab$$
Variable on Both Sides
For:
$$ax+b=cx+d$$
collect variable terms on one side and constants on the other.
One-Third of a Number
If the number is $$x$$:
$$\frac{x}{3}$$
Perimeter of a Rectangle
$$P=2(l+b)$$
where $$l$$ is length and $$b$$ is breadth.
Length 5 More Than Breadth
If breadth is $$x$$:
$$l=x+5$$
Verification
Substitute the obtained value into the original equation and check equality.
Related Practice Questions
Q1. Solve:
$$5x+4=3x+18$$
Q2. Solve:
$$\frac{x}{5}+2=8$$
Q3. The sum of a number and half of it is 30. Find the number.
Q4. A number is 4 more than twice another number. If the larger number is 20, find the smaller number.
Q5. The perimeter of a rectangle is 60 cm. Its length is 4 cm more than its breadth. Find both dimensions.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$5x+6=3x+18$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Find $$x$$:
$$\frac{x}{5}+4=10$$
A) $$20$$
B) $$25$$
C) $$30$$
D) $$35$$
Q3. The sum of a number and one-half of it is 27. The number is:
A) $$16$4
B) $$18$$
C) $$20$$
D) $$22$$
Q4. A number is 6 more than twice another number. If the larger number is 24, the smaller number is:
A) $$8$$
B) $49$$
C) $$10$$
D) $$12$$
Q5. A rectangle has perimeter 44 cm. If its length is 4 cm more than its breadth, its breadth is:
A) $$8$$ cm
B) $$9$$ cm
C) $$10$$ cm
D) $$12$$ cm
Exam Tips
✔ Clear fractions before solving whenever necessary.
✔ When variables appear on both sides, collect them carefully.
✔ Define the unknown quantity before forming a word-problem equation.
✔ Use correct perimeter formulas in geometry-based equations.
✔ Check whether the answer satisfies the original conditions.
✔ Carefully distinguish between “twice”, “half”, and “one-third”.
✔ Always check units in measurement problems.
Quick Revision Notes
✔ $$\frac{x}{a}=b$$ gives:
$$x=ab$$
✔ Variables on both sides should be collected on one side.
✔ One-half of $$x$$:
$$\frac{x}{2}$$
✔ One-third of $$x$$:
$$\frac{x}{3}$$
✔ Rectangle perimeter:
$$P=2(l+b)$$
✔ If length is 5 more than breadth:
$$l=b+5$$
✔ Verification confirms the solution.
Common Mistakes Students Make
❌ Forgetting to multiply by the denominator when solving a fractional equation.
❌ Moving variable terms incorrectly.
❌ Confusing one-third with three times.
❌ Using the wrong perimeter formula.
❌ Forgetting that “5 more than” means addition.
❌ Ignoring units in geometry questions.
❌ Not verifying the final result.
Key Takeaways
✔ Equations may contain variables on both sides.
✔ Fractional equations can be solved using inverse operations.
✔ Number relationships can be represented algebraically.
✔ Geometry formulas can be converted into equations.
✔ Word problems require careful definition of variables.
✔ Verification helps ensure the answer is correct.
FAQs
Q. How do we solve $$\frac{x}{4}+3=8$$?
Answer:
Subtract $$3$$:
$$\frac{x}{4}=5$$
Then multiply by $$4$$:
$$x=20$$
Q. What is one-third of a number $$x$$?
Answer:
One-third of $$x$$ is:
$$\frac{x}{3}$$
Q. What is the perimeter of a rectangle?
Answer:
The perimeter is:
$$P=2(l+b)$$
where $$l$$ is length and $$b$$ is breadth.
Q. What does “7 more than twice a number” mean?
Answer:
If the number is $$x$$, twice the number is $$2x$$, and 7 more than it is:
$$2x+7$$
Q. Why are variables useful in word problems?
Answer:
Variables allow unknown quantities to be represented mathematically so that equations can be formed and solved.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on fractional equations, variables on both sides, number relationships, and geometry-based application questions.
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