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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, age problems, and practical applications.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 7
Difficulty Level: Moderate to Difficult
Based On: NCERT Syllabus
Introduction
Simple equations provide a powerful method for finding unknown quantities. In many mathematical situations, a quantity is unknown but its relationship with other known quantities is given.
For example:
$$2x-5=17$$
Here, $x$ represents the unknown quantity. By using inverse operations, we can determine its value.
In Practice Set 7, students will solve fresh MCQs involving equations with variables on both sides, fractions, number relationships, and real-life application-based problems.
What You Will Learn
✔ Solving equations with variables on both sides
✔ Solving equations involving fractions
✔ Forming equations from verbal statements
✔ Solving number-based problems
✔ Applying equations to practical situations
✔ Verifying solutions
Why This Topic Is Important
Simple equations are an important foundation of algebra. They teach students how to represent unknown quantities mathematically and solve them using logical steps.
These concepts are useful for school examinations, word problems, and advanced algebraic topics 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:
$$6x-5=3x+16$$
A) $$5$$
B) $46$$
C) $47$$
D) $$8$$
Answer:
C) $$7$$
Useful Concept
When the variable appears on both sides, collect the variable terms on one side and the constant terms on the other side.
Solution
Given:
$$6x-5=3x+16$$
Subtract $$3x$$ from both sides:
$$6x-3x-5=16$$
$$3x-5=16$$
Add $$5$$ to both sides:
$$3x=21$$
Divide both sides by $$3$$:
$$x=7$$
Verification
Substitute $$x=7$$:
Left side:
$$6(7)-5=42-5=37$$
Right side:
$$3(7)+16=21+16=37$$
Therefore:
$$37=37$$
Hence, the solution is correct.
Correct Answer: C) $$7$$
Q2. Find the value of $$x$$:
$$\frac{x}{3}+5=12$$
A) $$18$$
B) $$21$$
C) $$24$$
D) $$27$$
Answer:
B) $$21$$
Useful Concept
First remove the constant term and then multiply by the denominator.
Solution
Given:
$$\frac{x}{3}+5=12$$
Subtract $$5$$ from both sides:
$$\frac{x}{3}=7$$
Multiply both sides by $$3$$:
$$x=21$$
Verification
$$\frac{21}{3}+5=7+5=12$$
Therefore, the solution is correct.
Correct Answer: B) $$21$$
Q3. The difference between twice a number and 7 is 19. Find the number.
A) $$11$$
B) $$12$$
C) $$13$$
D) $$14$$
Answer:
C) $$13$$
Useful Concept
“Twice a number” means $$2x$$, and “the difference between twice the number and 7” is represented by:
$$2x-7$$
Solution
Let the number be:
$$x$$
According to the question:
$$2x-7=19$$
Add $$7$$ to both sides:
$$2x=26$$
Divide by $$2$$:
$$x=13$$
Verification
$$2(13)-7=26-7=19$$
Therefore, the number is:
$$13$$
Correct Answer: C) $$13$$
Q4. The sum of two consecutive even numbers is 46. What is the smaller number?
A) $$20$$
B) $$22$$
C) $$24$$
D) $$26$$
Answer:
B) $$22$$
Useful Concept
Two consecutive even numbers differ by $$2$$. If the smaller even number is $$x$$, the next even number is:
$$x+2$$
Solution
Let the smaller even number be:
$$x$$
The next consecutive even number is:
$$x+2$$
Their sum is $$46$$:
$$x+(x+2)=46$$
Simplify:
$$2x+2=46$$
Subtract $$2$$:
$$2x=44$$
Divide by $$2$$:
$$x=22$$
Therefore, the smaller number is:
$$22$$
Verification
The two numbers are:
$$22,\ 24$$
Their sum is:
$$22+24=46$$
Hence, the answer is correct.
Correct Answer: B) $$22$$
Q5. A school bag costs ₹120 more than a notebook. If the total cost of the bag and notebook is ₹840, what is the cost of the notebook?
A) ₹320
B) ₹340
C) ₹360
D) ₹380
Answer:
C) ₹360
Useful Concept
When one quantity is a fixed amount more than another, represent the larger quantity as:
$$x+\text{fixed amount}$$
Solution
Let the cost of the notebook be:
$$x$$
The school bag costs ₹120 more:
$$x+120$$
The total cost is ₹840:
$$x+(x+120)=840$$
Simplify:
$$2x+120=840$$
Subtract $$120$$:
$$2x=720$$
Divide by $$2$$:
$$x=360$$
Therefore, the cost of the notebook is:
$$₹360$$
The cost of the bag is:
$$360+120=₹480$$
Verification
$$₹360+₹480=₹840$$
Therefore, the answer is correct.
Correct Answer: C) ₹360
Important Formulas & Concepts
Variable on Both Sides
For an equation such as:
$$ax+b=cx+d$$
collect variable terms on one side and constants on the other.
Fractional Equation
For:
$$\frac{x}{a}=b$$
we get:
$$x=ab$$
where $a\ne0$.
Twice a Number
If the number is $$x$$:
$$2x$$
Consecutive Even Numbers
If the smaller even number is $$x$$, the next consecutive even number is:
$$x+2$$
Consecutive Odd Numbers
If the smaller odd number is $$x$$, the next consecutive odd number is:
$$x+2$$
Fixed Difference
If one quantity is $$k$$ more than another quantity:
$$x+k$$
Verification
Substitute the obtained value into the original equation and check whether both sides are equal.
Related Practice Questions
Q1. Solve:
$$7x-4=4x+17$$
Q2. Find $$x$$:
$$\frac{x}{4}+6=11$$
Q3. The difference between three times a number and 8 is 28. Find the number.
Q4. The sum of two consecutive even numbers is 54. Find the numbers.
Q5. One book costs ₹50 more than another book. Their total cost is ₹450. Find the cost of each book.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Solve:
$$5x-3=2x+15$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Find $$x$$:
$$\frac{x}{4}+3=9$$
A) $$20$$
B) $$24$$
C) $$28$$
D) $$32$$
Q3. The difference between twice a number and 5 is 21. The number is:
A) $$11$$
B) $$12$$
C) $$13$$
D) $$14$$
Q4. Two consecutive even numbers have a sum of 62. The smaller number is:
A) $$28$$
B) $$30$$
C) $$32$$
D) $$34$$
Q5. A pen costs ₹20 more than a pencil. Together they cost ₹100. The cost of the pencil is:
A) ₹30
B) ₹40
C) ₹50
D) ₹60
Exam Tips
✔ When variables occur on both sides, collect them carefully on one side.
✔ For fractional equations, remove the fraction using multiplication.
✔ Remember that consecutive even or odd numbers differ by $$2$$.
✔ Translate “more than” into addition.
✔ Define the unknown quantity before forming a word-problem equation.
✔ Check your answer by substituting it into the original equation.
✔ Keep units such as ₹, cm, and years in application-based questions.
Quick Revision Notes
✔ Variable on both sides:
$$ax+b=cx+d$$
Collect variable terms on one side.
✔ Fraction:
$$\frac{x}{a}=b\Rightarrow x=ab$$
✔ Twice a number:
$$2x$$
✔ Consecutive even numbers:
$$x,\ x+2$$
✔ Consecutive odd numbers:
$$x,\ x+2$$
✔ $k$ more than $$x$$:
$$x+k$$
✔ Verification:
Substitute the answer into the original equation.
Common Mistakes Students Make
❌ Treating consecutive even numbers as numbers differing by $$1$$.
❌ Forgetting to remove the constant before solving a fractional equation.
❌ Confusing “more than” with subtraction.
❌ Moving terms between sides incorrectly.
❌ Forgetting units in word problems.
❌ Not checking the final answer.
Key Takeaways
✔ Equations can contain variables on both sides.
✔ Fractions can be handled using inverse operations.
✔ Consecutive even and odd numbers differ by $$2$$.
✔ Word problems can be converted into simple equations.
✔ Cost and quantity relationships can be represented algebraically.
✔ Verification is an important step in solving equations.
FAQs
Q. How are consecutive even numbers represented?
Answer:
If the first even number is $$x$$, the next consecutive even number is:
$$x+2$$
For example, $$12$$ and $$14$$ are consecutive even numbers.
Q. How do we solve $$\frac{x}{3}+5=12$$?
Answer:
Subtract $$5$$:
$$\frac{x}{3}=7$$
Then multiply by $$3$$:
$$x=21$$
Q. What does “twice a number” mean?
Answer:
If the number is $$x$$, twice the number is:
$$2x$$
Q. How do we represent a quantity that is ₹120 more than $$x$$?
Answer:
It is represented as:
$$x+120$$
Q. Why should we verify an equation?
Answer:
Verification confirms that the value obtained 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 even numbers, number relationships, and practical cost-based problems.
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