You might be solving ages problems from a long time. As you know, for qualifying competitive exams with better marks, we need to solve questions as quickly as possible. So for that we need to learn new tricks to solve questions as fast as possible. So for solving Ages problems quickly, here is a shortcut method that will help you solve this type of questions.

Here is an example.

The ratio of ages of father and son is 3:1. Four years earlier, the ratio was 4:1. What are the present ages of both father and son?

Solution:

Shortcut formula is below

Father:son

Present age= x:y

P years before= a:b

Then son’s age= [yP(a-b)/(difference of cross product)]

Father’s age= [xP(a-b)/(difference of cross product)]

Note: difference of cross product= xb-ay or ay-xb

Remember to subtract smaller from larger so that difference of cross product always comes positive.

Solve this question.

The answer will be

Son’s age= {1*4(4-1)}/{(4*1)-(3*1)} = 12 years

Father’s age= {3*4(4-1)}/{(4*1)-(3*1)} = 36 years

The same formula can be applied to Age problems in which later is given.

Here is an example.

The ratio of ages of father and son is 3:1. Four years later/after, the ratio will be 2:1. What are the present ages of both father and son?

Solution:

Shortcut formula is below

Father: son

Present age= x:y

P years later/after= a:b

Then son’s age= [yP(a-b)/(difference of cross product)]

Father’s age= [xP(a-b)/(difference of cross product)]

Note: difference of cross product= same as in above example

Shortcut trick #2

Example

The sum of ages of son and father is 56 years. After 4 years, the age of father will be 3 times the age of son. Determine son’s age?

Solution:

Let the age of son be x years

Then the age of father is 56-x years

After 4 years,

the age of father will be 3 times the age of son. It means

3(x+4)= 56-x+4

this equation is made by adding 4 years to ages of both son and father. Then we have to equalize the equation by multiplying 3 to the son’s age because it is given that after 4 years, the age of father will be 3 times the age of son.

Now solving the above equation,

3x+12= 60-x

3x+x= 60-12

4x= 48

x=12 years

son’s age= 12 years Ans.