Aptitude - Problems on Ages - Discussion
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.
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).
Why do we complicate it by taking Divya's age = 2*S?
take, Divya=D.
Shurthi=S.
5 years hence,so;
D+5/S+5 = 9/5.
we get, 5D+25 = 9S+45(take this as equation 1).
and TEN YEARS BACK,so;
D-10/S-10 = 3/1.
we get, D-10 = 3S-30(take this as equation 2).
Now substitute equation * in equation 1 and solve ,we get S=20
Now substitute S = 20 in equation 2 ,we get D=40.
So now we got D=40 and S=20, so the ratio is 1:2.