Study Material ā 15 PYQs (2018ā2018) Ā· Concept Notes Ā· Shortcuts
SSC MTS Linear Equations is a frequently tested subtopic ā 15 previous year questions from 2018ā2018 papers are included below with concept notes, key rules and shortcut tricks.
A man is 5 times as old as his son. If the sum of their ages is 48 years, what is the son's age?
Exam Q 92018Previous Year Pattern
The sum of two consecutive integers is 37. What is the larger integer?
Exam Q 102018Previous Year Pattern
If 5x - 3 = 2(x + 6), then the value of 3x + 2 is:
Exam Q 112018Previous Year Pattern
A number is such that when 12 is subtracted from it, the result is 8 less than half the original number. What is the number?
Exam Q 122018Previous Year Pattern
The sum of three consecutive odd numbers is 57. If the smallest number is increased by 12 and the largest is decreased by 6, what is the sum of the new three numbers?
Exam Q 132018Previous Year Pattern
If 3(2x + 5) = 4(x - 2) + 35, find the value of x.
Exam Q 142018Previous 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. Find the son's current age.
Exam Q 152018Previous Year Pattern
A fraction becomes 1/2 when 2 is subtracted from its numerator and 1 is added to its denominator. The fraction becomes 2/3 when 1 is added to both numerator and denominator. Find the original fraction.
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