Question

The age of a father is 3times the age of his son 5years ago father was 5times as old as his son was their present ages are?

Answer 1

Let the present age of father and his son be x and y respectively.

According to the question,

• Case 1

⇒ Age of father is 3 times the age of his son

∴ x = 3y ⇒ x - 3y = 0 ...(1)

Also,

• Case 2

⇒ 5 years ago, father was 5 times old as his son

∴ (x - 5) = 5(y - 5) [∵ we are given information about 5 years ago, So we need to subtract 5 from both ages ]

⇒ x - 5 = 5y - 25

⇒ x - 5y = -20 ...(2)

Subtract (1) from (2)

⇒ x - 5y - (x - 3y) = -20 - 0

⇒ x - 5y - x + 3y = -20

⇒ -2y = -20

⇒ y = 10

Substituting [y = 10] in (1), we get

⇒ x - 3×10 = 0

⇒ x = 30

Hence,

Father's present age is 30 years

Son's present age is 10 years

Note :- Always assume present ages in these type of questions. and subtract the number of years given if given past information. For Example:

If it is given that x's age was 3 times of y's age 5 years ago, Then it would be expressed as:

⇒ x - 5 = 5(y - 3)

Solving further,

⇒ x - 5y = 2