Study Material — 26 PYQs (2018–2021) · Concept Notes · Shortcuts
AFCAT Linear Equations is a frequently tested subtopic — 26 previous year questions from 2018–2021 papers are included below with concept notes, key rules and shortcut tricks.
The sum of two numbers is 48 and their difference is 14. What is the larger number?
Exam Q 102021Previous Year Pattern
If 2x - 5 = x + 3, what is the value of x?
Exam Q 112021Previous Year Pattern
Solve for y: 5y - 12 = 2y + 9
Exam Q 122021Previous Year Pattern
A number when multiplied by 6 and then reduced by 8 equals 40. Find the number.
Exam Q 132021Previous Year Pattern
The sum of two consecutive even numbers is 54. What is the larger of the two numbers?
Exam Q 142021Previous Year Pattern
If 5(2x - 3) = 3(x + 4), then x equals:
Exam Q 152021Previous Year Pattern
If 3x + 7 = 2x + 15, then the value of x is:
Exam Q 162021Previous Year Pattern
Two numbers are in the ratio 5:7. If their sum is 120, what is the larger number?
Exam Q 172020Previous Year Pattern
Rajesh has some money. If he spends ₹240, he will have 3/5 of his original amount left. How much money does Rajesh currently have?
Exam Q 182021Previous Year Pattern
A man is 4 times as old as his son. After 8 years, he will be 3 times as old as his son. What is the son's current age?
Exam Q 192021Previous Year Pattern
A man is 4 times as old as his son. If the sum of their ages is 60 years, how old is the son?
Exam Q 202021Previous Year Pattern
Three times a number decreased by 8 equals 19. What is the number?
Exam Q 212021Previous Year Pattern
If (2x - 3)/5 = (x + 1)/3, then x equals:
Exam Q 222021Previous Year Pattern
If 3(x + 2) = 2(x + 5) + 4, then the value of x is:
Exam Q 232018Previous Year Pattern
If 3x + 4y = 18 and 4x + 3y = 17, find the value of (x + y)² + (x − y)².
Exam Q 242021Previous Year Pattern
A man is 4 times as old as his son. In 6 years, the man will be 3 times as old as his son. If the man's current age is M years and his son's current age is S years, find the value of M + S.
Exam Q 252021Previous Year Pattern
A fraction becomes 1/2 when 1 is subtracted from both numerator and denominator. The same fraction becomes 2/3 when 8 is added to both numerator and denominator. What is the original fraction?
Exam Q 262021Previous Year Pattern
Two numbers are in the ratio 5:7. If 8 is subtracted from each, the resulting numbers are in the ratio 2:3. Find the sum of the original two numbers.
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
The sum of two consecutive integers is 47. What is the larger integer?
Practice 14medium
A man is 4 times as old as his son. After 8 years, he will be 2.5 times as old as his son. What is the son's current age?
Practice 15medium
A man is 4 times as old as his son. If the sum of their ages is 60 years, how old is the son?
Practice 16medium
If 3x + 7 = 2x + 12, then the value of x is:
Practice 17medium
A man is 6 years older than his wife. Five years ago, the product of their ages was 391. If the man's current age is M years, which of the following equations correctly represents this situation?
Practice 18medium
The sum of two consecutive even numbers is 86. What is the larger of the two numbers?
Practice 19medium
If 5x - 3 = 2x + 9, then 3x + 2 equals:
Practice 20medium
A number is divided into two parts such that one part is 5 more than the other. If the number is 23, what is the smaller part?
2 more practice questions in the Study Panel
Difficulty-graded, bookmarkable, with timed mode. Free account — no credit card.