Aptitude - Problems on Ages - Discussion
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 3x years and 4x 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 = 3x can be found. Thus, I and II give the answer.
From I and III, we get 4x = 3x + 5. This gives x.
Tanya's age = 3x 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.
Tanya's age after 5 years and not the present age as mentioned above is assumed to be 't' years.
If Tanya's present age be 't' tears as mentioned above, then on solving with statement II we get 't' i.e. the present age to be 20. This contradicts the solution from the first two statements.
Hence Statement 1 is true 3:4.
After 5 years 20 and 25 Hence 4:5 is also true.
Rahul is 5 years older than Tanya is True.
Then present ratio will (3x+5)/(4x+5) = 4/5, on solving we get x = 5.
Then there age will 15, 20.
So the answer E is correct.
So Rahul is 5 years than Tanya,
So all statements correct.
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.