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Placement Preparation
**Specialization:
**Quantitative Aptitude**Offline Downloads:
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Important Formulas Shortcuts 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 = x + n.
3. If the current age is x, then age n years ago = x - n.
4. The ages in a ratio of a : b will be ax and bx.
5. If the current age is x, then 1/n of the age is x/n.
Question: t1 yrs earlier the father’s age was x times that of his son. At
present the father’s age is y times that of his son. What are the present
ages of the son and the father?
Formula
Questions: The present age of the father is y times the age of his son. t2 yrs
hence, the father’s age become z times the age of his son. What are the
present ages of the father and his son?
Formula

Questions: t1 yrs earlier, the age of the father was x times the age of his
son. t2 yrs hence, the age of the father becomes z times the age of his son.
What are the present ages of the son and the father?
Formula
Note : Do you get the similarities between the above two direct methods? They differ
only in sign in the numerator. When the question deals with „ago‟, a +ve sign exixts and
when it deals with „after‟, a –ve sign exists in the numerator.
Solutions. 6:
Then what formula comes?
Father
:
Son
Present age =
x
:
y
After T yrs=
a
:
b
Then, Son‟s age =
And, Father‟s age =

Note:
1. While evaluating the difference of cross-product, always take +ve sign.
2. Both the above direct formulas look similar. The only difference you can find is in the
denominators. But it has been simplified as “difference of cross-products” to make it
easier to remember. So, with the help of one formula only you can solve both the
question.
3. We suggest you to go-through both the methods and choose the better of the two.

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