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Age / Quant-Reasoning puzzles questions for IPMAT, with solutions
10 free Age / Quant-Reasoning puzzles practice questions for IPMAT Indore, Rohtak and JIPMAT, each with the answer and a full worked solution. No sign-in. Try each one first, then open the solution. The lessons for this chapter are in Age / Quant-Reasoning puzzles on Learn.
Question 1Multiple choiceWritten by IPMATwayAge relation puzzles
The sum of the present ages of A and B is 55 years. Five years ago A was twice as old as B. What is A's present age?
- A.40 years
- B.45 years
- C.35 years
- D.30 years
Show the answer and solution
Answer: C. 35 years
Answer: (C) 35 years
Working:
- With a = 55 - b: 50 - b = 2b - 10, so b = 20.
- A is 35.
Why the others are wrong:
- (A) 40 years does not satisfy the conditions in the stem when checked back.
- (B) 45 years does not satisfy the conditions in the stem when checked back.
- (D) 30 years does not satisfy the conditions in the stem when checked back.
Question 2Multiple choiceWritten by IPMATwayAge relation puzzles
Five years ago the sum of the ages of two brothers was 30 years. What will be the sum of their ages 10 years from now?
- A.55 years
- B.65 years
- C.60 years
- D.50 years
Show the answer and solution
Answer: C. 60 years
Answer: (C) 60 years
Working:
- Their sum now is 30 + 10 = 40.
- In 10 years it is 40 + 20 = 60.
Why the others are wrong:
- (A) 55 years does not satisfy the conditions in the stem when checked back.
- (B) 65 years does not satisfy the conditions in the stem when checked back.
- (D) 50 years does not satisfy the conditions in the stem when checked back.
Question 3Multiple choiceWritten by IPMATwayAge relation puzzles
What is the present age of Priya?
I. Priya's age is 4 times her age 9 years ago. II. Priya is younger than her brother.
- A.Statement I alone is sufficient, but statement II alone is not sufficient
- B.Statement II alone is sufficient, but statement I alone is not sufficient
- C.Both statements together are sufficient, but neither alone is sufficient
- D.Both statements together are not sufficient
Show the answer and solution
Answer: A. Statement I alone is sufficient, but statement II alone is not sufficient
Answer: (A) Statement I alone is sufficient, but statement II alone is not sufficient
Working:
- I alone: p = 4p - 36, so p = 12. II gives only a comparison.
Why the others are wrong:
- (B) This verdict does not match what the statements fix.
- (C) This verdict does not match what the statements fix.
- (D) This verdict does not match what the statements fix.
Question 4Multiple choiceWritten by IPMATwayAge relation puzzles
Ten years ago A was 3 times as old as B. Ten years from now A will be twice as old as B. What is A's present age?
- A.90 years
- B.70 years
- C.60 years
- D.80 years
Show the answer and solution
Answer: B. 70 years
Answer: (B) 70 years
Working:
- a = 3b - 20 and a = 2b + 10, so b = 30 and a = 70.
Why the others are wrong:
- (A) 90 years does not satisfy the conditions in the stem when checked back.
- (C) 60 years does not satisfy the conditions in the stem when checked back.
- (D) 80 years does not satisfy the conditions in the stem when checked back.
Question 5Multiple choiceWritten by IPMATwayAge relation puzzles
The average age of a husband, his wife and their child 3 years ago was 27 years. The average age of the wife and the child 5 years ago was 20 years. What is the husband's present age?
- A.40 years
- B.35 years
- C.45 years
- D.50 years
Show the answer and solution
Answer: A. 40 years
Answer: (A) 40 years
Working:
- Now the three total 81 + 9 = 90.
- Wife and child now total 40 + 10 = 50.
- Husband = 90 - 50 = 40.
Why the others are wrong:
- (B) 35 years does not satisfy the conditions in the stem when checked back.
- (C) 45 years does not satisfy the conditions in the stem when checked back.
- (D) 50 years does not satisfy the conditions in the stem when checked back.
Question 6Multiple choiceWritten by IPMATwayAge relation puzzles
Rakesh married 10 years ago at the age of 27; his wife was 23 then. Six years after the marriage the average age of Rakesh, his wife and their son was 22 years. After how many years of the marriage was the son born?
- A.3 years
- B.4 years
- C.6 years
- D.2 years
Show the answer and solution
Answer: D. 2 years
Answer: (D) 2 years
Working:
- Six years after marriage: Rakesh 33, wife 29, total 66, so the son was 4.
- He was born 6 - 4 = 2 years after the marriage.
Why the others are wrong:
- (A) 3 years does not satisfy the conditions in the stem when checked back.
- (B) 4 years does not satisfy the conditions in the stem when checked back.
- (C) 6 years does not satisfy the conditions in the stem when checked back.
Question 7Multiple choiceWritten by IPMATwayAge relation puzzles
A is twice as old as B, and B is 5 years older than C. The sum of their ages is 55 years. What is A's age?
- A.20 years
- B.25 years
- C.35 years
- D.30 years
Show the answer and solution
Answer: D. 30 years
Answer: (D) 30 years
Working:
- B = c + 5 and A = 2c + 10.
- The sum 4c + 15 = 55 gives c = 10.
- A is 30.
Why the others are wrong:
- (A) 20 years does not satisfy the conditions in the stem when checked back.
- (B) 25 years does not satisfy the conditions in the stem when checked back.
- (C) 35 years does not satisfy the conditions in the stem when checked back.
Question 8Multiple choiceWritten by IPMATwayAge relation puzzles
The present ages of A and B are in the ratio 5 : 3. After 6 years the ratio will be 7 : 5. What is the sum of their present ages?
- A.16 years
- B.32 years
- C.40 years
- D.24 years
Show the answer and solution
Answer: D. 24 years
Answer: (D) 24 years
Working:
- 5k and 3k: 5(5k + 6) = 7(3k + 6) gives k = 3.
- Ages 15 and 9, sum 24.
Why the others are wrong:
- (A) 16 years does not satisfy the conditions in the stem when checked back.
- (B) 32 years does not satisfy the conditions in the stem when checked back.
- (C) 40 years does not satisfy the conditions in the stem when checked back.
Question 9Multiple choiceWritten by IPMATwayAge relation puzzles
What is the present age of Meena?
I. Meena is twice as old as her daughter and the sum of their ages is 60 years. II. Meena was 24 when her daughter was born.
- A.Statement I alone is sufficient, but statement II alone is not sufficient
- B.Statement II alone is sufficient, but statement I alone is not sufficient
- C.Both statements together are sufficient, but neither alone is sufficient
- D.Both statements together are not sufficient
Show the answer and solution
Answer: A. Statement I alone is sufficient, but statement II alone is not sufficient
Answer: (A) Statement I alone is sufficient, but statement II alone is not sufficient
Working:
- I alone: 3d = 60, d = 20, Meena 40. II gives only the gap of 24 years.
Why the others are wrong:
- (B) This verdict does not match what the statements fix.
- (C) This verdict does not match what the statements fix.
- (D) This verdict does not match what the statements fix.
Question 10Multiple choiceWritten by IPMATwayAge relation puzzles
Four years ago, the ratio of Ravi's age to his mother's age was 1 : 5. Eight years from now, the ratio will be 3 : 7. When Ravi becomes as old as his mother was at the time he was born, what will be the ratio of Ravi's age to his mother's age?
- A.5 : 17
- B.3 : 7
- C.1 : 2
- D.17 : 29
Show the answer and solution
Answer: C. 1 : 2
Answer: (C) 1 : 2
Working:
- Four years ago let Ravi be k and his mother 5k. Eight years from now (12 years after that) they are k + 12 and 5k + 12.
- (k + 12)/(5k + 12) = 3/7 → 7k + 84 = 15k + 36 → k = 6. So Ravi is 10 and his mother 34 today.
- The age gap is always 24, so his mother was 24 when Ravi was born.
- Ravi turns 24 in 14 years; his mother will then be 48. Ratio 24 : 48 = 1 : 2.
Why the others are wrong:
- (A) 5 : 17 is the ratio of their present ages (10 : 34), not the ratio at the later time.
- (B) 3 : 7 is the ratio eight years from now, which is given in the question.
- (D) Takes the target as Ravi reaching his mother's PRESENT age (34), giving 34 : 58; the question asks for her age when he was born (24).