# Aptitude - Problems on Ages - Discussion

*Directions to Solve*

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

What is the present age of Tanya? | |

I. | The ratio between the present ages of Tanya and her brother Rahul is 3 : 4 respectively. |

II. | After 5 years the ratio between the ages of Tanya and Rahul will be 4 : 5. |

III. | Rahul is 5 years older than Tanya. |

I. Let the present ages of Tanya and Rahul be 3*x* years and 4*x* years.

II. After 5 years, (Tanya's age) : (Rahul's age) = 4 : 5.

III. (Rahul's age) = (Tanya's age) + 5.

From I and II, we get | 3x + 5 |
= | 4 | . This gives x. |

4x + 5 |
5 |

Tanya's age = 3*x* can be found. Thus, I and II give the answer.

From I and III, we get 4*x* = 3*x* + 5. This gives *x*.

Tanya's age = 3*x* can be found. Thus, I and III give the answer.

From III : Let Tanya's present age be *t* years.

Then Rahul's present age = (*t* + 5) years.

Thus, from II and III, we get : | t | = | 4 | . This gives t. |

t + 5 |
5 |

Thus, II and III give the answer.

Correct answer is (E).

Let me explain;

Equation 1 and 2 & 2 and 3 will give the future after 5 years age.

i.e tania :20 year and rahul : 25 , because both consist equation 2 (which says after 5 years )

Whereas equation 1 will give the present age,

i,e. tania :15 , rahul : 20.

Hope you all get it , good day.

The correct answer will be (I, II & III) because,

3:4, we can take as 15 & 20.

4:5, as 20 & 25.

And here Rahul is 5 years older than Taniya.

So Rahul is 5 years than Tanya,

So all statements correct.

So the answer E is correct.

Then present ratio will (3x+5)/(4x+5) = 4/5, on solving we get x = 5.

Then there age will 15, 20.