# AGE PROBLEMS WITH SOLUTION AND SHORTCUT TRICK

Age Problems Shortcut Trick
Dear reader,
Welcome to resultmerit.com. 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 quickly.

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.