# Aptitude - Problems on Ages

- Problems on Ages - Formulas
- Problems on Ages - General Questions
- Problems on Ages - Data Sufficiency 1
- Problems on Ages - Data Sufficiency 2
- Problems on Ages - Data Sufficiency 3

*Directions to Solve*

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

- Give answer (A) 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.
- Give answer (B) 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.
- Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
- Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
- Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

What is Sonia's present age? | |

I. | Sonia's present age is five times Deepak's present age. |

II. | Five years ago her age was twenty-five times Deepak's age at that time. |

I. S = 5D D = | S | ....(i) |

5 |

II. S - 5 = 25 (D - 5) S = 25D - 120 ....(ii)

Using (i) in (ii), we get S = | 25 x | S | - 120 | ||

5 |

4S = 120.

S = 30.

Thus, I and II both together give the answer. So, correct answer is (E).

Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year? | |

I. | Retirement age is 60 years. |

II. | There are 50 employees in the department. |

I. Retirement age is 60 years.

II. There are 50 employees in the department.

Average age of 50 employees = 30 years.

Total age of 50 employees = (50 x 30) years = 1500 years.

Number of employees next year = 40.

Total age of 40 employees next year (1500 + 40 - 60 x 10) = 940.

Average age next year = | 940 | years = 23 | 1 | years. |

40 | 2 |

Thus, I and II together give the answer. So, correct answer is (E).

Divya is twice as old as Shruti. What is the difference in their ages? | |

I. | Five years hence, the ratio of their ages would be 9 : 5. |

II. | Ten years back, the ratio of their ages was 3 : 1. |

Let Divya's present age be D years and Shruti's present age b S years

Then, D = 2 x S D - 2S = 0 ....(i)

I. | D + 5 | = | 9 | ....(ii) |

S + 5 | 5 |

II. | D - 10 | = | 3 | ....(iii) |

S - 10 | 1 |

From (ii), we get : 5D + 25 = 9S + 45 5D - 9S = 20 ....(iv)

From (iii), we get : D - 10 = 3S - 30 D - 3S = -20 ....(v)

Thus, from (i) and (ii), we get the answer.

Also, from (i) and (iii), we get the answer.

I alone as well as II alone give the answer. Hence, the correct answer is (C).