Study Material ā 17 PYQs (2018ā2018) Ā· Concept Notes Ā· Shortcuts
SBI Clerk Linear Equations is a frequently tested subtopic ā 17 previous year questions from 2018ā2018 papers are included below with concept notes, key rules and shortcut tricks.
The sum of two consecutive integers is 47. What is the larger integer?
Exam Q 92018Previous 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 102018Previous Year Pattern
The difference between two numbers is 18. If the larger number is 5 times the smaller number, what is the smaller number?
Exam Q 112018Previous Year Pattern
If 5(x - 2) = 3(x + 4), then x equals:
Exam Q 122018Previous Year Pattern
A number when multiplied by 3 and then reduced by 8 gives 16. What is the number?
Exam Q 132018Previous Year Pattern
A man is 4 times as old as his son. After 6 years, he 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 142018Previous Year Pattern
Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, and Train Y travels from B towards A at 40 km/h. At what distance from station A will they meet?
Exam Q 152018Previous Year Pattern
A shopkeeper sells two items. Item P is sold at a profit of 25%, and Item Q is sold at a loss of 20%. If the cost price of Item P is ā¹800 and the cost price of Item Q is ā¹600, and the shopkeeper wants an overall profit of 10% on the combined cost price, how much additional amount (in ā¹) must be added to the selling prices to achieve this target?
Exam Q 162018Previous Year Pattern
Three numbers are in the ratio 2:3:5. If a certain value is added to each number, the new ratio becomes 4:5:7. If the original sum of the three numbers is 100, what is the value that was added to each number?
Exam Q 172018Previous Year Pattern
A sum of money is divided among A, B, and C in the ratio 3:4:5. If ā¹200 is transferred from C to A, the new ratio becomes 5:4:3. What is the original sum of money?
Concept Notes
Linear Equationsā Rules & Concept
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Core Concept
Read this first ā the foundation of the topic
āCore 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
š”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.
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Formula Block
Memorise ā at least one formula appears in every paper
ā¢ One variable: ax + b = 0, solution x = -b/a
ā¢ Two variables: a1x + b1y = c1 and a2x + b2y = c2
ā¢ Elimination method: Multiply equations to make coefficients equal
ā¢ Substitution method: Express one variable in terms of another
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Exam Patterns
What examiners ask ā 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.
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Shortcuts
Use these to save 30ā60 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.
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Worked Example
Solve this step-by-step before moving on
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Step 1
Let the numbers be x and y where x > y
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Step 2
Given equations are x + y = 50 and x - y = 12
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Step 3
Using shortcut - Larger number = (50+12)/2 = 31
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Step 4
Smaller number = (50-12)/2 = 19
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Step 5
Verification: 31 + 19 = 50 ā and 31 - 19 = 12 ā
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