CAT Linear Equations Questions 2026: Concepts, Shortcuts & Practice Set

Overview: CAT Linear Equations Questions are an important part of Quantitative Ability preparation for CAT exam 2026. These questions test your algebraic clarity, equation formation, and ability to convert word-based information into mathematical expressions. Although the concept is basic, CAT often presents linear equations through age problems, ratios, mixtures, numbers, percentages, and work-related situations.

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For CAT exam syllabus 2026, focus on understanding how to form equations quickly rather than merely solving them mechanically. Strong command over linear equations can also improve your performance in Arithmetic, Algebra, and Number Systems.

What Are CAT Linear Equations?

A linear equation is an equation in which the highest power of the variable is 1. For example:

3x + 5 = 20

Here, x = 5.

A linear equation in two variables may look like this:

2x + 3y = 12

CAT Linear Equations Questions may involve one equation, a pair of equations, or multiple conditions that must first be translated into equations. In CAT exam pattern 2026, such questions are likely to appear as direct Algebra questions or as application-based questions from Arithmetic.

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25+ CAT Linear Equations Questions to Practice

Q1. Solve for x: 5x − 17 = 3x + 9

A. 11

B. 12

C. 13

D. 14

Answer: C. 13

Q2. If 7x + 4 = 3x + 28, find x.

A. 5

B. 6

C. 7

D. 8

Answer: B. 6

Q3. Solve: 4(x − 3) = 2(x + 5)

A. 10

B. 11

C. 12

D. 13

Answer: B. 11

Q4. Solve: (3x/4) + 5 = 14

A. 10

B. 11

C. 12

D. 13

Answer: C. 12

Q5. If 2x + 7 = 5x − 11, find x.

A. 5

B. 6

C. 7

D. 8

Answer: B. 6

Q6. If x + y = 18 and x − y = 6, find x.

A. 10

B. 11

C. 12

D. 13

Answer: C. 12

Q7. Solve: 2x + 3y = 19 and 2x − y = 3. Find y.

A. 3

B. 4

C. 5

D. 6

Answer: B. 4

Q8. Solve: 3x + 2y = 16 and x + y = 7. Find x.

A. 1

B. 2

C. 3

D. 4

Answer: B. 2

Q9. If 4x + 5y = 33 and 2x − y = 1, find x + y.

A. 6

B. 7

C. 8

D. 9

Answer: B. 7

Q10. Solve: 5x − 2y = 14 and 3x + 2y = 18. Find x.

A. 3

B. 4

C. 5

D. 6

Answer: B. 4

Q11. The sum of two numbers is 46 and their difference is 12. Find the larger number.

A. 27

B. 28

C. 29

D. 30

Answer: C. 29

Q12. The sum of the present ages of A and B is 42 years. Five years ago, A was twice as old as B. Find A’s present age.

A. 27 years

B. 28 years

C. 29 years

D. 30 years

Answer: C. 29 years

Q13. A father is 30 years older than his son. After 10 years, the father will be twice the age of his son. Find the son’s present age.

A. 10 years

B. 12 years

C. 14 years

D. 16 years

Answer: A. 10 years

Q14. The present age of a mother is four times the age of her daughter. After 8 years, the mother will be twice the age of her daughter. Find the daughter’s present age.

A. 4 years

B. 6 years

C. 8 years

D. 10 years

Answer: A. 4 years

Q15. The sum of the digits of a two-digit number is 11. The tens digit exceeds the units digit by 3. Find the number.

A. 47

B. 56

C. 65

D. 74

Answer: D. 74

Q16. The sum of a two-digit number and the number obtained by reversing its digits is 121. If the tens digit is 3 more than the units digit, find the original number.

A. 47

B. 56

C. 74

D. 83

Answer: C. 74

Q17. A two-digit number is 27 more than the number formed by reversing its digits. If the sum of its digits is 9, find the number.

A. 54

B. 63

C. 72

D. 81

Answer: B. 63

Q18. The ratio of boys to girls in a class is 3:4. If 6 boys leave and 2 girls join, the ratio becomes 1:2. Find the original number of students.

A. 56

B. 63

C. 70

D. 77

Answer: C. 70

Q19. The ratio of incomes of A and B is 5:4, while the ratio of their expenditures is 3:2. If each saves ₹6,000, find A’s income.

A. ₹20,000

B. ₹25,000

C. ₹30,000

D. ₹35,000

Answer: C. ₹30,000

Q20. A mixture contains milk and water in the ratio 5:2. If 14 litres of water are added, the ratio becomes 5:4. Find the original quantity of the mixture.

A. 35 litres

B. 42 litres

C. 49 litres

D. 56 litres

Answer: C. 49 litres

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Q21. A shopkeeper mixes rice costing ₹40 per kg and ₹60 per kg to obtain a mixture worth ₹48 per kg. Find the ratio of cheaper rice to costlier rice.

A. 2:3

B. 3:2

C. 3:5

D. 5:3

Answer: B. 3:2

Q22. A person buys 3 pens and 2 notebooks for ₹94. Another person buys 2 pens and 3 notebooks for ₹91. Find the cost of one pen.

A. ₹17

B. ₹19

C. ₹20

D. ₹22

Answer: C. ₹20

Q23. Two tickets of type A and three tickets of type B cost ₹460. Three tickets of type A and two tickets of type B cost ₹440. Find the price of one type A ticket.

A. ₹80

B. ₹90

C. ₹100

D. ₹110

Answer: C. ₹100

Q24. A and B together can complete a task in 12 days. A alone can complete it in 20 days. In how many days can B alone complete the task?

A. 24 days

B. 28 days

C. 30 days

D. 36 days

Answer: C. 30 days

Q25. A taxi charges a fixed amount plus a charge per kilometre. A 10 km journey costs ₹180, while a 16 km journey costs ₹252. Find the fixed charge.

A. ₹40

B. ₹50

C. ₹60

D. ₹70

Answer: C. ₹60

Q26. The perimeter of a rectangle is 54 cm. Its length is 3 cm more than twice its breadth. Find its breadth.

A. 7 cm

B. 8 cm

C. 9 cm

D. 10 cm

Answer: B. 8 cm

Q27. The cost of 5 apples and 3 oranges is ₹135, while the cost of 3 apples and 5 oranges is ₹125. Find the cost of one apple.

A. ₹15

B. ₹17

C. ₹20

D. ₹22

Answer: C. ₹20

Q28. A number is increased by 20% and then decreased by 10%. The final value is 108. Find the original number.

A. 90

B. 95

C. 100

D. 105

Answer: C. 100

Q29. The sum of three consecutive integers is 93. Find the largest integer.

A. 30

B. 31

C. 32

D. 33

Answer: C. 32

Q30. In a test, each correct answer carries 4 marks and each incorrect answer carries −1 mark. A student attempted 30 questions and scored 75 marks. Find the number of correct answers.

A. 20

B. 21

C. 22

D. 23

Answer: B. 21

Why Are CAT Linear Equations Questions Important for CAT 2026?

CAT Linear Equations Questions are often embedded within Arithmetic and Number System problems rather than appearing only as direct Algebra questions. A question involving ages, ratios, mixtures, profit and loss, or digits can become much easier once the right equation is formed.

Practising CAT Linear Equations Questions helps you improve equation formation, logical interpretation, calculation speed, and accuracy in multi-step questions. Since this topic overlaps with several CAT Quant questions and chapters, it can contribute to stronger overall performance in CAT 2026.

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Key Concepts Required for CAT Linear Equations Questions

Linear Equation in One Variable

The standard form is:

ax + b = 0, where a ≠ 0.

For example, 5x - 15 = 0 gives x = 3.

Linear Equations in Two Variables

The standard form is:

ax + by + c = 0

For example, 3x + 2y = 18. One equation with two variables has infinitely many solutions. You need at least two independent equations to find unique values of x and y.

Pair of Linear Equations

A pair of equations can be written as:

a₁x + b₁y = c₁

a₂x + b₂y = c₂

CAT Linear Equations Questions commonly require substitution, elimination, or comparison to solve such pairs.

Methods to Solve CAT Linear Equations Questions 2026

1. Substitution Method

Use substitution when one variable can be expressed easily in terms of the other.

Example: If x + y = 12 and x - y = 4, find x and y.

From x + y = 12, x = 12 - y.

Substituting into x - y = 4:

12 - y - y = 4

2y = 8, so y = 4 and x = 8.

2. Elimination Method

Elimination is often faster when the coefficients of one variable can be made equal quickly.

Example: Solve 2x + 3y = 17 and 2x - y = 5.

Subtracting the second equation from the first gives 4y = 12. Therefore, y = 3 and x = 4.

3. Comparison Method

Use comparison when both equations can be rearranged conveniently.

Example: If x = 2y + 3 and x = 5y - 6, equate both expressions:

2y + 3 = 5y - 6

Therefore, y = 3.

Common Types of Linear Equations Questions for CAT 2026

Age-Based Questions

Age questions use present, past, and future relationships. Assign variables to present ages first, then convert every condition into an equation.

Number-Based Questions

These questions involve digits, number reversal, digit sums, and divisibility conditions. For a two-digit number, use 10x + y, where x is the tens digit and y is the units digit.

Ratio and Proportion Questions

For a ratio such as 3:5, assume the quantities are 3k and 5k. This reduces the number of variables and makes equation formation faster.

Mixture and Alligation Questions

Mixture problems often use weighted-average equations. Express total cost as the sum of the costs of individual quantities.

Work and Time Questions

Work problems can be converted into linear equations by using work rates. If a person completes a task in n days, their one-day work is 1/n.

CAT Linear Equations Questions 2026: Advanced Shortcuts

Translate Words Into Symbols Immediately

• Five more than twice a number = 2x + 5
• Three less than a number = x - 3
• A is 20% more than B = A = 1.2B
• The ratio of A to B is 3:5 = A = 3k and B = 5k

Use Elimination Before Substitution

When coefficients are simple, elimination is usually faster. Look for equations where a variable can be cancelled through addition or subtraction.

Check Practical Restrictions

In digit, age, and quantity questions, verify whether the answer is practical. Digits must be between 0 and 9, ages cannot be negative, and quantities should follow the conditions given in the question.

Avoid Solving More Than Required

If the question asks for x + y or a ratio, do not calculate individual values unless required. This can save valuable time in CAT 2026.

CAT Linear Equations Questions PDF: How to Use It Effectively

A CAT linear equations questions PDF can be useful when you practise in a structured manner. Start with direct equations, then move to application-based questions involving ages, numbers, ratios, mixtures, and work.

1. Concept Practice: Solve direct questions on one-variable and two-variable equations.
2. Application Practice: Solve age, number, ratio, mixture, and work-based questions.
3. Timed Practice: Attempt mixed CAT-level questions within a fixed time limit and analyse your errors.

A CAT linear equations questions PDF should help you understand equation formation and identify shorter methods, not simply increase your question count.

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Linear Equations Questions for CAT 2026: 7-Day Practice Plan

Day	Topic	Practice Target
Day 1	One-variable equations	25 questions
Day 2	Two-variable equations	25 questions
Day 3	Substitution and elimination	20 questions
Day 4	Age and number problems	20 questions
Day 5	Ratio, mixture, and percentage problems	20 questions
Day 6	Work, time, and mixed applications	20 questions
Day 7	Timed test and error analysis	25 questions

Common Mistakes to Avoid in CAT Linear Equations Questions 2026

• Misinterpreting terms such as “more than,” “less than,” “at least,” and “at most”
• Using an incorrect base value while calculating percentages
• Forgetting practical restrictions in age and digit questions
• Creating too many variables when one variable is enough
• Solving equations without checking whether they are independent
• Spending too much time on lengthy word problems

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How to Choose Linear Equations Questions in CAT 2026

In CAT 2026, select Linear Equations Questions where the variables and conditions are clear within the first few seconds. Prioritise questions in which you can form equations quickly and see an obvious route to elimination or substitution.

If a question involves too many unknowns, vague conditions, or lengthy calculations, move on initially and revisit it only if time permits. Good and important CAT topic selection is as important as solving ability in CAT Quant.

Conclusion

CAT Linear Equations Questions are valuable because they develop the algebraic thinking required across Quantitative Ability. Focus on equation formation, learn when to use substitution or elimination, and practise application-based questions regularly.

Use a CAT linear equations questions PDF for organised practice, but prioritise accuracy, method selection, and error analysis. With consistent revision and timed practice, Linear Equations Questions for CAT can become a dependable scoring area for CAT 2026.