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?
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?
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?
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 =
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.