#### Ages

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**

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**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 **

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**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.

#### ages concept

**Concept | Practice set 1 | Practice set 2**

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