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

The current ages of two direct cousins follow a base proportion of 3 : 5. Exactly 5 years from the current moment, the proportion ratio of their ages updates to 2 : 3. Find the current age of the elder cousin.

  1. 15 years

  2. 20 years

  3. 25 years

  4. 30 years

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

Let the ages be 3x and 5x. Five years later, the ages are 3x+5 and 5x+5. The ratio is (3x+5)/(5x+5) = 2/3. Cross-multiplying gives 9x+15 = 10x+10, so x=5. The elder cousin's current age is 5x = 25.

Multiple choice

Rohan's age after 8 years will be two-fifths of his father Mahesh's age at that time. 12 years ago, the ratio of their ages was 1 : 4. What is Mahesh's present age?

  1. 72 yr

  2. 84 yr

  3. 88 yr

  4. 92 yr

  5. 96 yr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R and M be their present ages. After 8 years, R+8 = 2/5(M+8). 12 years ago, (R-12)/(M-12) = 1/4. Solving this system: 4R-48 = M-12 => M = 4R-36. Substituting into the first equation: 5(R+8) = 2(4R-36+8) => 5R+40 = 8R-56 => 3R = 96 => R = 32. Then M = 4(32)-36 = 128-36 = 92.

Multiple choice

Directions: In the following question, two statements labelled I and II are given. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and give your answer from the given options. What is the ratio of the present ages of Deepak and Ankit? I. 10 years ago the ratio of Deepak's age to Ankit's age was 2 : 1. II. Deepak is 10 years older than Ankit.

  1. Statement I alone is sufficient, but statement II alone is not sufficient.

  2. Statement II alone is sufficient, but statement I alone is not sufficient.

  3. Both statements I and II together are sufficient, but none of the statements alone is sufficient.

  4. Either statement I or statement II alone is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D and A be present ages. I: (D-10)/(A-10) = 2/1 -> D-10 = 2A-20 -> D = 2A-10. II: D = A+10. Combining: A+10 = 2A-10 -> A = 20, D = 30. Ratio 30:20 = 3:2. Both are needed.

Multiple choice

Each question below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer- (1) If the question can be answered by using statement I alone but cannot be answered by statement II alone. (2) If the question can be answered by using statement II alone but cannot be answered by statement I alone. (3) If both statements I and II together are required to answer the question. (4) If the answer can be found by using any of the two statements alone. (5) If both the statements together are not sufficient to answer the question.What is the age of Ravi at present? I. His present age is 4 times the present age of Ram. II. Five years ago Ravi's age was 7 times the age of Ram. .

  1. 1

  2. 2

  3. 3

  4. 4

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

Statement I gives the relation V = 4M, which is not sufficient alone. Statement II gives V - 5 = 7(M - 5), which is also not sufficient alone. Combining both statements gives a unique solution (Ram is 10 and Ravi is 40), so both statements together are required.

Multiple choice

Each question below is followed by two statements A and B. You have to determine whether the data given in the statement 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 statement A alone is sufficient to answer the question, but the statement B alone is not sufficient. (b)if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient. (c)if the both statement A and B together are needed to answer the question. (d)if either the statement A alone or B alone is sufficient to answer the question. (e)if you cannot get the answer from the statements A and B together, but needed even more data.What will be Suraj's age after eight years? A. The ratio between Kamya's and Suraj's present age is 4 : 7 respectively. B. Kamya is 15 yr younger than Suraj.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

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

Statement A gives a ratio (4:7), which doesn't provide absolute ages. Statement B gives a difference (15 years). Together, let ages be 4x and 7x. 7x - 4x = 15 -> 3x = 15 -> x = 5. Suraj's age is 35, so after 8 years he is 43. Both are needed.

Multiple choice

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: What is the present age of Sanjeev?I. Sanjeev is 4 years younger than Anuj. The ratio of the age of Anuj and Vipin is 4 : 5.II. Vipin is 1 year older than Sanjeev and the present age of Anuj is 20 years.III. The present age of Sanjeev is 5 years less than the age of Mohan.

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

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

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

  4. The data in all the statements I, II and III are not sufficient to answer the question.

  5. The data in all the statements I, II and III together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I relates Sanjeev and Anuj. Statement II provides Anuj's age and relates Vipin to Sanjeev. Together, they allow us to find Sanjeev's age (Anuj=20, Sanjeev=20-4=16). Statement III provides another way to find the age if Mohan's age were known, but it is not needed given I and II.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: The ratio of the present age of Prem and Pravin is 8:7. After 10 years the ratio of Prem and his son is 3:1. Sum of the present age of Prem and his son's age after 4 years is 40 years. Then find the Pravin's present age? Quantity II: The present age of mother is two years less than thrice the age of her daughter. After two years the mother's age will be 10 years more than twice the age of her daughter. What is the present age of mother?

  1. Quantity I > Quantity II

  2. Quantity II > Quantity I

  3. Quantity I ≥ Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot beestablished
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Prem/Pravin = 8x/7x. Prem+10 / (Son+10) = 3/1. Prem + (Son+4) = 40. Solving these yields Pravin's age as 21. Quantity II: M = 3D - 2. (M+2) = 2(D+2) + 10. Solving yields M = 25. Since 25 > 21, Quantity II > Quantity I.

Multiple choice

Directions: The following problem consists of a question followed two statements I and II, giving certain data. Select the correct answer from the given options depending on the sufficiency of data given in the statements to answer the question. Mark answer (1) if statement I alone is sufficient and statement II alone is not sufficient to answer the question. (2) if statement II alone is sufficient and statement I alone is not sufficient to answer the question. (3) if both statements I and II together are sufficient but neither statement alone is sufficient to answer the question. (4) if both statements I and II together are not sufficient to answer the question and additional data specific to the question is needed. What is the present age of Sushma, if she is 20 years older than her son? (I) After 16 years, she will be twice old as her son. (II) Three years ago, Sushma's age was 7 times the age of her daughter.

  1. 1

  2. 2

  3. 3

  4. 4

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

Statement I: S = s + 20 and S + 16 = 2(s + 16). This is a system of two equations with two variables, which is sufficient to solve for S.

Multiple choice

Directions: The following questions are accompanied by three statements A, B and C. You have to determine which statement(s) is/are sufficient necessary to answer the questions and mark your answer accordingly. What is the present age of Arun? (A) Eight years ago, age of Ankit is same as Aman's present age while four years hence, age of Ankit will be same as Arun's present age. (B) Four years ago, ratio of Aman's age and Arun's age is 4:7 (C) Present age of Arun is 60% more than present age of Aman.

  1. Any two of them

  2. Either A and B or B and C

  3. Either A or B and C together

  4. Any one of them

  5. Either A and B or A and C
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Ankit = K, Aman = M, Arun = R. (A) gives K-8 = M and K+4 = R. (B) gives (M-4)/(R-4) = 4/7. (C) gives R = 1.6M. Using A and C: R = 1.6M, K = M+8, R = K+4 = M+8+4 = M+12. So 1.6M = M+12, 0.6M = 12, M = 20, R = 32. Using A and B: K = M+8, R = K+4 = M+12. (M-4)/(M+12-4) = 4/7 => 7M-28 = 4M+32 => 3M = 60 => M=20, R=32. Both pairs (A,C) and (A,B) are sufficient.

Multiple choice

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: What is the sum of the age of Ram and Mohan? Statement I: The age of Ram is 6 years more than the age of Mohan. Statement II: 40% of the age of Mohan is equal to 30% of the age of Ram. Statement III: The ratio between half of the age of Ram and one third of the age of Mohan is 2:1.

  1. Either statement III alone or statements I and II together are sufficient.

  2. Only statement III is sufficient.

  3. Only statement I and II is sufficient.

  4. Only statement I, II, and III are sufficient.

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

[CAT 2002] Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then what is the age of the younger boy?

  1. 3

  2. 4

  3. 2

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be x and y (x < y < 10). x = cuberoot(xy). x^3 = xy, so x^2 = y. If x=2, y=4. Father's age = 24. Mother's age = (42/2) = 21. Difference = 24 - 21 = 3. This matches the condition.

Multiple choice

Directions: In the following question, a given questions is followed by information in three statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. Find the present age of B? Statement I - Age A 2years ago equal to the age of C 4years ago. Age of C is average age of A and B. Statement II - ratio of present age of B and age of C after 2 years is 1:1. A is 2 years younger than C.

  1. Only Statement I alone.

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives relationships among A, B, and C but does not fix their absolute ages. Statement II also gives only relative relationships, and using both statements still leaves the ages undetermined. Therefore, neither statement is sufficient.

Multiple choice

Directions: In the following question, a given questions is followed by information in three statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. What is the present age of D? Statement I - Ratio between present age of M and D is5:13. M is 9 year younger than P. Statement II - P's age after 9 year will be 33 years. The difference between D's age and M's age is same as the present age of P.

  1. Only Statement I alone.

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: M/D = 5/13, M = P-9. Statement II: P+9 = 33 => P=24. D-M = P = 24. We have M = 24-9 = 15. Then 15/D = 5/13 => D = 39. Both statements are needed.

Multiple choice

Directions: Study the following information carefully and answer the questions given below: There are ten members in a family of four generation having three married couples. V is the child of T. P is uncle of N who has only one sibling. M is grandfather of S who is only child of R. O is married and older than N. V is grandson of N and has only one sibling. T is daughter-in-law of N. Q is sister of N. O is mother of N. R is grandmother of U. U is not sister of V. O has no siblings. If O is 55 years old and S is 30 years old, then what may be the possible age of R?

  1. 29 years

  2. 45 years

  3. 58 years

  4. Cant' be determined

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

R is grandmother of U, and S is only child of R. Since there are four generations and three married couples, and O is 55, R is likely in the generation above O or the same. Given the family structure and ages, 45 is a reasonable age for R if she is in the generation of O.