Aptitude - Problems on Ages - Discussion

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"The secret to creativity is knowing how to hide your sources."

- Albert Einstein

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.

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.

[A].	I alone sufficient while II alone not sufficient to answer
[B].	II alone sufficient while I alone not sufficient to answer
[C].	Either I or II alone sufficient to answer
[D].	Both I and II are not sufficient to answer
[E].	Both I and II are necessary to answer

Answer: Option C

Explanation:

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).

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Aptitude - Problems on Ages - Discussion

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