SSC GD Constable Linear Equations — Study Material, 15 PYQs & Practice MCQs | ZestExam
ZestExam
SSC GD Constable Linear Equations
Study Material — 15 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC GD Constable Linear Equations is a frequently tested subtopic — 15 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
A number is such that when 8 is subtracted from it and the result is multiplied by 3, we get 24. What is the number?
Exam Q 82018Previous Year Pattern
If 3x + 7 = 2x + 12, find the value of x.
Exam Q 92018Previous Year Pattern
A man's age is 3 times his son's age. After 10 years, his age will be twice his son's age. What is the son's current age?
Exam Q 102018Previous Year Pattern
If 2(3x + 4) - 5 = 3(2x - 1) + 8, what is the value of x?
Exam Q 112018Previous Year Pattern
The sum of two consecutive integers is 47. Find the larger integer.
Exam Q 122018Previous Year Pattern
A man invests ₹5000 in two schemes. In scheme X, he gets 8% simple interest per annum, and in scheme Y, he gets 10% simple interest per annum. After 2 years, the total interest earned is ₹900. How much did he invest in scheme X?
Exam Q 132018Previous Year Pattern
A train travels from station A to station B. If it increases its speed by 20%, it reaches 1 hour earlier. If it decreases its speed by 25%, it reaches 2 hours later. Find the original time taken (in hours) to travel from A to B.
Exam Q 142018Previous Year Pattern
Two numbers are in the ratio 3:4. If 8 is added to the first number and 2 is subtracted from the second, the ratio becomes 5:6. Find the sum of the original two numbers.
Exam Q 152018Previous Year Pattern
A man is 5 times as old as his son. After 10 years, he will be 3 times as old as his son. If the man's current age is M and his son's current age is S, find M + S.
Concept Notes
Linear Equations— Rules & Concept
💡
Core Concept
Read this first — the foundation of the topic
→Core Concept
Linear equations represent straight lines when plotted on a graph. In SSC CGL, you'll mostly deal with one variable (like x) or two variables (like x and y). The key is finding the value of unknown variables
💡Key Rules
For one variable linear equations like ax + b = 0, the solution is x = -b/a. For two variable systems, you need two equations to find unique solutions. Always maintain balance - whatever you do to one side, do to the other side.
🔢
Formula Block
Memorise — at least one formula appears in every paper
• One variable: ax + b = 0, solution x = -b/a
• Two variables: a1x + b1y = c1 and a2x + b2y = c2
• Elimination method: Multiply equations to make coefficients equal
• Substitution method: Express one variable in terms of another
📊
Exam Patterns
What examiners ask — read before attempting PYQs
SSC CGL loves testing linear equations through word problems. Age problems, mixture problems, and number problems frequently appear. Questions often involve finding two numbers given their sum and difference, or determining speeds and distances. Expect 2-3 questions per paper.
⚡
Shortcuts
Use these to save 30–60 seconds per question
For sum-difference problems, use this lightning method. If sum = S and difference = D, then larger number = (S+D)/2 and smaller number = (S-D)/2. This skips the entire equation-solving process.
✏️
Worked Example
Solve this step-by-step before moving on
1
Step 1
Let the numbers be x and y where x > y
2
Step 2
Given equations are x + y = 50 and x - y = 12
3
Step 3
Using shortcut - Larger number = (50+12)/2 = 31
4
Step 4
Smaller number = (50-12)/2 = 19
5
Step 5
Verification: 31 + 19 = 50 ✓ and 31 - 19 = 12 ✓
Answer: The numbers are 31 and 19.
Another Trick: For age problems, always define variables for present ages. If the problem mentions 'after n years' or 'before n years', add or subtract n from present ages respectively.
Common Mistake: Students often confuse the setup in word problems. Read carefully whether the problem asks for present age or future age. Also, many forget to verify their answers by substituting back into original equations. Always cross-check your solutions to avoid silly errors that cost marks in competitive exams.
Key Points to Remember
Linear equation has highest power of variable as 1
For ax + b = 0, solution is x = -b/a
Two equations needed to solve two unknown variables