Today I'm going to discuss some problems based on ages. These are an important questions regarding bank exams and other competitive exams. To solve the problems related to ages, You will require knowledge of linear equations. I have tried to evaluate some easy and quick method for you people to solve these types of questions.
Consider the following example:
Example: The age of father 2 years ago 7 times the age of his son. At present, fathers age is five times that of his son . What are the ages of father and son at present?
Solution: Let present age of son = `x`
present age of father = `y`
Start with the present age son
Then read the question and write the given equations.
Last step, Just make an equation using values of father's age.
Either, convert it both into present ages or 2 years ago
2years ago, `7(x2)` = `5x2`.............................................. 5x is present age of father. I converted it into age before 2 years
So equation is, `7(x2) = (5x2)`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `5 times 6` = `30` yrs
Example2: The age of father after 2 years is 4 times the age of his son. At present, father's age is five times that of his son . What are the ages of father and son at present?
Solution: The difference between both of examples is just ,one is 2 yrs ago and other is 2yrs hence.
Let present age of son = `x` yrs and
present age of father = `y` yrs
Similarly, make an equation using values of father's age.
Either, convert it both into present ages or 2 years ago
2years hence, `4(x+ 2)` = `5x+2`.............................................. 5x is present age of father. I converted it into age after 2 years
So equation is, `4(x+2) = (5x+2)`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `5 times 6` = `30` yrs.
Example3: 2 yrs earlier father's age was 7 times the age of his son. 2 years hence father's age would be 4 times the age of his son. What are the present ages of father and son?
Solution: Let present age of son = `x` yrs and
present age of father = `y` yrs
Making an equation using values of father's age.
2years ago, `7(x2)` = `4(x+2) 4`
Here,4(x+2) is age after two years.Therefore, I converted it into age before 2 years by subtracted 4 years.
So equation is, `7(x2)` =`4(x+2)4`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `7(x2)` + 2 (i.e. age before 2 years + 2 = present age)
⇒ `7(4) + 2` = `28 +2` = `30`yrs.
Shortcut of these three examples are very simple. Must try it once as it saves your time in exams. You should definitely try this once. But if you are not comfortable then you can do with the previous method.
Also check: Tricks of ratio and proportions
Some important points
 Assume the present ages, then proceed with the equations.
 While making equations, always remember to convert both sides into either present year or the given year i.e. time frame should be same.
 5 years ago `to`present year  5 years
 5 years hence `to` present year + 5 years
Consider the following example:
Example: The age of father 2 years ago 7 times the age of his son. At present, fathers age is five times that of his son . What are the ages of father and son at present?
Solution: Let present age of son = `x`
present age of father = `y`
Age 2 years ago

Present age


Son

`x`  2

`x`

Father

`7(x2)`

`y = 5x`

Start with the present age son
Then read the question and write the given equations.
Last step, Just make an equation using values of father's age.
Either, convert it both into present ages or 2 years ago
2years ago, `7(x2)` = `5x2`.............................................. 5x is present age of father. I converted it into age before 2 years
So equation is, `7(x2) = (5x2)`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `5 times 6` = `30` yrs
Example2: The age of father after 2 years is 4 times the age of his son. At present, father's age is five times that of his son . What are the ages of father and son at present?
Solution: The difference between both of examples is just ,one is 2 yrs ago and other is 2yrs hence.
Let present age of son = `x` yrs and
present age of father = `y` yrs
Present age

Age after 2 years
 
Son

`x`

`x+2`

Father

`y = 5x`

`4(x+2)`

Similarly, make an equation using values of father's age.
Either, convert it both into present ages or 2 years ago
2years hence, `4(x+ 2)` = `5x+2`.............................................. 5x is present age of father. I converted it into age after 2 years
So equation is, `4(x+2) = (5x+2)`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `5 times 6` = `30` yrs.
Example3: 2 yrs earlier father's age was 7 times the age of his son. 2 years hence father's age would be 4 times the age of his son. What are the present ages of father and son?
Solution: Let present age of son = `x` yrs and
present age of father = `y` yrs
Age 2 years ago

Present age

Age 2 years hence


Son

`x – 2`

`x`

`x+2`

Father

`7(x2)`

`y`

`4(x+2)`

Making an equation using values of father's age.
2years ago, `7(x2)` = `4(x+2) 4`
Here,4(x+2) is age after two years.Therefore, I converted it into age before 2 years by subtracted 4 years.
So equation is, `7(x2)` =`4(x+2)4`
Solving equation, x =`6` yrs
Therefore, present age of son = `6`yrs and
present age of father = `7(x2)` + 2 (i.e. age before 2 years + 2 = present age)
⇒ `7(4) + 2` = `28 +2` = `30`yrs.
Shortcut of these questions:
Age 2 years ago

Present age

Age 2 years hence


Father’s
age as compared to son

7

5

4

1) `2 times (71)/(75)`
2) `2 times (41)/(54)`
3) `(2 times (71) + 2times (41))/ (74)`
Shortcut of these three examples are very simple. Must try it once as it saves your time in exams. You should definitely try this once. But if you are not comfortable then you can do with the previous method.
Also check: Tricks of ratio and proportions