Algebra — CAT Previous Year Questions

How many CAT questions come from Algebra?

Algebra has contributed 181 questions to Common Admission Test papers between 2017 and 2025 — an average of about 20 questions a year. That count is measured from EByAi’s bank of 6,737 CAT questions, not estimated from a syllabus. Every one of the 181 questions carries a written, step-by-step solution, and each is tagged to Algebra within Quant, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Algebra questions from real CAT papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 181 Algebra questions (with full written solutions) are available in practice.

1. Question 1 · CAT 2024

   When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
   1. (A)4 : 3
   2. (B)2 : 1
   3. (C)3 : 2
   4. (D)5 : 4
   Show answerAnswer

   Answer: (D) 5 : 4

2. Question 2 · CAT 2024

   A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
   1. (A)1 : 27
   2. (B)1 : 81
   3. (C)1 : 26
   4. (D)1 : 80
   Show answerAnswer

   Answer: (D) 1 : 80

3. Question 3 · CAT 2023

   All of the following statements are evidence of the decline of liberalism today, EXCEPT:
   1. (A)". . . the creation of a business aristocracy, the rise of vast companies . . ."
   2. (B)"And technological advances are reducing ever more areas of work into meaningless drudgery."
   3. (C)"Democracy has degenerated into a theatre of the absurd."
   4. (D)"'The gap between liberalism's claims about itself and the lived reality of the citizenry' is now so wide that 'the lie can no longer be accepted,'. . ."
   Show answerAnswer

   Answer: (B) "And technological advances are reducing ever more areas of work into meaningless drudgery."

4. Question 4 · CAT 2023

   Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to
   1. (A)42%
   2. (B)47%
   3. (C)45%
   4. (D)49%
   Show answerAnswer

   Answer: (B) 47%

5. Question 5 · CAT 2023

   Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be
   1. (A)17
   2. (B)21
   3. (C)16
   4. (D)20
   Show answerAnswer

   Answer: (B) 21

Algebra questions by year

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More CAT Quant chapters

• Arithmetic (259)
• Geometry (87)
• Number System (79)
• Modern Maths (48)

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