Problems on Ages | Quantitative Aptitude Basic Formula


Important Formulas on “Problems on Ages” :
1. If the current age is x, then n times the age is nx.
2. If the current age is x, then age n years later/hence = x + n.
3. If the current age is x, then age n years ago = x – n.
4. The ages in a ratio a : b will be ax and bx.
5. If the current age is x, then 1/n of the age is x/n

Example
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.

1.
What is Sonia’s present age?
I.Sonia’s present age is five times Deepak’s present age.
 II.Five years ago her age was twenty-five times Deepak’s age at that time.
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 E
Explanation:

 I. S = 5D     D =S….(i)
5
II. S – 5 = 25 (D – 5)     S = 25D – 120 ….(ii)
Using (i) in (ii), we get S =open_ph_left25 xSopen_ph_right- 120
5
 4S = 120.
 S = 30.
Thus, I and II both together give the answer. So, correct answer is (E).
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