Study Material — 13 PYQs (2019–2019) · Concept Notes · Shortcuts
IBPS RRB PO Linear Equations is a frequently tested subtopic — 13 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.
IBPS RRB PO Linear Equations — Past Exam Questions
13 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution
Exam Q 12019Previous Year Pattern
If 2x + 3 = x + 9, then x equals:
Exam Q 22019Previous Year Pattern
The sum of two consecutive integers is 47. Find the larger integer.
Exam Q 32019Previous Year Pattern
If 6x - 8 = 4x + 12, what is the value of x?
Exam Q 42019Previous Year Pattern
A number when multiplied by 4 and then 5 is subtracted from the result gives 35. Find the number.
Exam Q 52019Previous Year Pattern
Solve for y: 3(y - 4) = 18
Exam Q 62019Previous Year Pattern
If 5x + 12 = 37, what is the value of x?
Exam Q 72019Previous Year Pattern
If 3x + 7 = 2x + 15, then the value of x is:
Exam Q 82019Previous Year Pattern
A shopkeeper sells two items. If the cost price of item A is ₹200 and the cost price of item B is ₹300, and he sells both at a total of ₹600, what is his overall profit or loss percentage?
Exam Q 92019Previous Year Pattern
The sum of two consecutive even numbers is 46. What is the larger number?
Exam Q 102019Previous 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 112019Previous Year Pattern
A shopkeeper marks goods at 60% above cost price. He gives a discount of 25% on the marked price. However, due to a calculation error, he mistakenly gives an additional 10% discount on the already discounted price to every customer. What is his net profit or loss percentage?
Exam Q 122019Previous Year Pattern
A man has some money. He spends 1/4 of it on food, 1/3 of the remaining on rent, and 1/2 of what still remains on utilities. After these expenses, he has ₹2,700 left. How much money did he initially have?
Exam Q 132019Previous Year Pattern
A man travels from City A to City B. If he increases his speed by 20%, he reaches 2 hours earlier. If he decreases his speed by 25%, he reaches 4 hours later. Find the actual time taken (in hours) to travel from A to B at normal speed.
Concept Notes
Linear Equations— Rules & Concept
Core ConceptRead 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 BlockMemorise — 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 PatternsWhat 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.
ShortcutsUse 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 ExampleSolve 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.
Exam TrapsCommon mistakes students make — avoid these
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