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Problems on Ages - General Aptitude

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.
Q1:

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

ANS:C - Either I or II alone sufficient to answer

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