Quantitative Aptitude

Problems on Ages

1,744 Questions
All Translate multiples, fractions, and percentages 518 Use two ratios from different dates 500 Convert an age ratio into actual ages 258 Handle averages and changing groups 167 Generational age chains 111 Recognize equal age gaps 101 Product of ages 68 Ages in arithmetic progression 11 Division of lifespan 9

Problems on Ages Questions

Multiple choice

Directions: The item given below consists of a question and two statements, numbered I and II. You have to decide whether the data provided in the statement is sufficient to answer the question. Read both the statements and choose the correct option. What is the present age of M? I. The ratio of age of M to the age of N is 3 : 4. Ten years ago, the age of M was half of N. II. The difference between the age of M and N is 10. Ten years from now, the ratio of the age of M to that of N will become 4 : 5.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both statement I and II together is necessary to answer the question.

  5. The data even in both statements I and II together is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: M/N = 3/4 and (M-10)/(N-10) = 1/2. This is a system of two equations with two variables, sufficient to solve for M. Statement II: |M-N| = 10 and (M+10)/(N+10) = 4/5. This is also a system of two equations, sufficient to solve for M.

Multiple choice

Given below are two statements: Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5. Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72. In the light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true. but Statement II is false.

  4. Statement I is false. but Statement II is true.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I: Let ages be x and 5x. x * 5x = 245 => 5x^2 = 245 => x^2 = 49 => x = 7. Ages are 7 and 35. After 9 years, ages are 16 and 44. Ratio 16:44 = 4:11, not 3:5. Statement I is false. Statement II: 70 milk, 30 water. Sell 1/5 (20L total), remaining 80L (56 milk, 24 water). Add 20L water. New mix: 56 milk, 44 water. Ratio water:milk = 44:56 = 11:14, not 28:72. Both are false.

Multiple choice

Rahul resides in Bangalore with his extended family, including his parents, grandparents, older brother and younger sister. Rahul successfully obtained his MBA degree from a prestigious business school in 2013. During that year, the collective age of his family members averaged 42 years. In 2015, Rahul entered matrimony, and a year later, he embraced fatherhood. Given that the average age of Rahul's family remained unchanged from 2013 to 2019, and considering that Rahul is four years older than his spouse, what was the age at which Rahul completed his MBA?

  1. 35 years

  2. 36 years

  3. 37 years

  4. 38 years

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The problem states the average age of the family remained unchanged from 2013 to 2019. This is only possible if the number of family members and their total age changes in a specific way, but the question asks for Rahul's age at MBA completion (2013). Given the constraints, 37 is the calculated result.

Multiple choice

Riya resides in Jaipur as a part of her extended family, including her parents, grandparents, elder brother, younger sister, and a cousin who is three years her junior. Riya accomplished her engineering degree in the year 2010 from a well-known university. During that year, the average age of Riya's family was 29. Riya got married in 2013 and, three years later, welcomed her first child. If the average age of Riya's 10-member family including Riya in 2018 increased by 5 years when it was compared with the average age of her family in 2010, and Riya is one year older than her spouse, at what age did Riya accomplished her engineering degree?

  1. 30 years

  2. 32 years

  3. 35 years

  4. 38 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: The question is followed by two statements, I and II. Answer the question using the following instructions. A. The question can be answered by using statement I alone but cannot be answered by using the other statement alone. B. The question can be answered by using statement II alone but cannot be answered by using the other statement alone. C. The question can be answered by using either of the statements alone. D. The question can be answered by using both the statements together but cannot be answered by using either of the statements alone. E. The question cannot be answered even by using both the statements together. What is the present age of J? I. Five years ago, the ratio of the age of J to that of L was 2 : 3. The difference between the ages of J and L is 3 years. II. The sum of the ages of J and K is 20. The difference between the ages of J and K is 4 years.

  1. A

  2. B

  3. C

  4. D

  5. E
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labeled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. What is the father's current age? (i) Three years ago, the father's age was four times his son's age. (ii) Four years from now, the father's age will be 3 years less than three times his son's age.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives F - 3 = 4(S - 3), which is one equation with two variables. Statement (2) gives F + 4 = 3(S + 4) - 3, another equation with two variables. Together, they form a system of two linear equations that can be solved for F and S.

Multiple choice

Directions: This question has two statements, (1) and (2). Answer the question using the following instructions: Today is Carol's birthday. How old is she? (1) 6 years ago she was half her present age. (2) 3 years from now she will be 3 times as old as she was 7 years ago.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but neither of them alone is sufficient

  4. if both statements (1) and (2) independently are sufficient

  5. if both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be her age. (1) x - 6 = 0.5x => 0.5x = 6 => x = 12. (2) x + 3 = 3(x - 7) => x + 3 = 3x - 21 => 2x = 24 => x = 12. Both statements independently give the same age.

Multiple choice

Directions: The problem below consists of a question and two statements numbered I and II given below it. Decide whether the data provided in the statements are sufficient to answer the question. Mark your answer as What is the ratio of present ages of father and his son? I. Ratio of the ages of father 20 years ago and son 10 years ago was 2 : 1. II. Sum of the present ages of father and son is 50 years.

  1. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question

  2. if the data in both statements I and II together are necessary to answer the question

  3. if the data in both statements I and II together are not sufficient to answer the question

  4. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: Read the following information carefully and answer the question. Seven brothers M, N, O, P, Q, R and S are of different ages, but not necessarily in the same order. S is younger than R. N is older than O. Four brothers are older than S. Q is not the youngest. R is older than O, but younger than P. Q and M are younger than O. Only one person was born between N and O. If N is 4 years older than O and M is 21 years old, what could be the age of P? (The age of the all the persons is in whole numbers)

  1. Not more than 29 years

  2. At least 29 years

  3. Exactly 29 years

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Directions: The question below is followed by two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. What is the difference between the ages of Madhu and Shweta? I. The sum of their ages is 75 years and their ages are in the ratio 3 : 2 or 2 : 3. II. Madhu is 45 years old and the respective ratio of ages of Shweta and Madhu is 2 : 3.

  1. Data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. Data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. Data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. Data given in both the statements I and II together is not sufficient to answer the question.

  5. Data given in both the statements I and II together is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I provides the sum (75) and the ratio (3:2 or 2:3), allowing us to find the ages (45 and 30) and their difference (15). Statement II provides Madhu's age (45) and the ratio of Shweta to Madhu (2:3), which allows us to find Shweta's age (30) and the difference (15). Both statements independently provide sufficient information.

Multiple choice

Each of the questions below consist of a question and two statements A, B and C given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. The ratio of the ages of Javed and Akhtar is 6 :11. Find out the ratio of their ages 5 years ago. A. The difference of their ages is 25 years. B. The difference of their ages after 5 years will be 25 years. C. The sum of their ages is 85 years.

  1. Only A and C together are sufficient

  2. Anyone of A, B and C is sufficient

  3. Only A and B together are sufficient

  4. Any two of A, B and C are sufficient

  5. All together are necessary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio 6:11 implies ages 6x and 11x. Any statement providing a difference or sum allows solving for x, which then allows calculating the ratio at any time point.

Multiple choice

Directions: In this problem, you have to find out which of the following statements is/are redundant for determining the answer of the given question or can be dispensed with. What will be the sum of the ages of mother and the daughter after 12 years? I. The mother's present age is 5/3 of the daughter's present age. II. After 5 years, the ratio of the mother's age to the daughter's age will become 8 : 5. III. The difference between the present ages of the mother and the daughter was equal to the daughter's age 10 years ago.

  1. Either I or II

  2. Either II or III

  3. Either I or III

  4. Any one of the three

  5. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M and D be present ages. I: M = 5/3 D. II: (M+5)/(D+5) = 8/5. III: M - D = D - 10. Each statement provides a unique linear relationship between M and D. Since we have two variables, any two of these three statements are sufficient to solve for M and D, meaning any one of them is redundant.

Multiple choice

Passage

Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer (a) if the question can be answered by using statement I alone but cannot be answered by statement II alone (b) if the question can be answered by using statement II alone but cannot be answered by statement I alone (c) if both statements I and II together are required to answer the question (d) if the answer can be found by using any of the two statements alone (e) if both the statements together are not sufficient to answer the question

Ratio of present ages of Rohit and Rahul is 2 : 3. Find Rahul's present age. I. Ratio of present ages of Rahul and Parul is 5 : 6. II. Parul's age is 8 years more than Rohit's age.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rohit:Rahul = 2:3. Statement I gives Rahul:Parul = 5:6. Statement II gives Parul = Rohit + 8. We have a system of equations: Rohit = 2x, Rahul = 3x, Parul = 6/5 * Rahul = 18x/5. Then 18x/5 = 2x + 8. This allows solving for x and thus Rahul's age. Both are required.

Multiple choice

Passage

Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer (a) if the question can be answered by using statement I alone but cannot be answered by statement II alone (b) if the question can be answered by using statement II alone but cannot be answered by statement I alone (c) if both statements I and II together are required to answer the question (d) if the answer can be found by using any of the two statements alone (e) if both the statements together are not sufficient to answer the question

How many times will the father be of his daughter's age after 5 years? I. The ratio of their ages after 4 years will be 2 : 1, respectively. II. The average of their ages is 41.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of ages at a future time, which is insufficient without current ages. Statement II gives the average age, which is also insufficient. Together, let F and D be current ages. (F+4)/(D+4) = 2/1 and (F+D)/2 = 41. This system of two equations with two variables allows solving for F and D, and thus the future ratio.

Multiple choice

Passage

Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer (a) if the question can be answered by using statement I alone but cannot be answered by statement II alone (b) if the question can be answered by using statement II alone but cannot be answered by statement I alone (c) if both statements I and II together are required to answer the question (d) if the answer can be found by using any of the two statements alone (e) if both the statements together are not sufficient to answer the question

Sum of Rohit, Parul and Priya's present ages is 53 years. Find Priya's present age. I. Priya is 2 years elder than Parul. ">II. Ratio of Rohit and Parul's present ages is 5 : 6, respectively and that of Parul and Priya is 9 : 10, respectively.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Rohit, Parul, Priya be R, P, A. R+P+A = 53. Statement II gives ratios R:P = 5:6 and P:A = 9:10. This allows expressing all in terms of one variable (e.g., P), which is sufficient to solve for all ages.