Question

Five years ago Rams mother was five times his age.If his mother is

now thrice as old as him , Find their present ages?​

Answer 1

Given :-

5 years ago, Ram's mother was five times his age

Ram's Mother is now thrice as old as him.

To find :-

Present age of Ram

Present age of Ram's mother

Solution :-

Let the present age of Ram be x years

Let the present age of Ram's mother be y years.

As per the first condition,

5 years ago, Ram's mother was five times his age

5 years ago,

Ram's age = x - 5

Mother's age = y - 5

Let's represent the first condition mathematically to get our first equation.

y - 5 = 5 ( x - 5)

y - 5 = 5x - 25

5x - 25 = y - 5

5x - y = - 5 + 25

5x - y = 20 -----> 1

As per the second condition,

If his mother is now thrice as old as him

Ram's age = 3x

Mother's age = y

Let's represent this too mathematically. Here we will get just the value of one of the variables, either x or y.

y = 3x

Substitute, y = 3x in equation 1,

5x - y = 20 ----> 1

Plug in the value of y,

5x - 3x = 20

2x = 20

x =
`\frac{20}2}`

x = 10

Present age of Ram = x = 10 years

Substitute, x = 10 in equation 1,

5x - y = 20 ---> 1

5 ( 10 ) - y = 20

50 - y = 20

- y = 20 - 50

- y = - 30

[canceling minus from both sides]

y = 30

Present age of Mother = y = 30 years

•°• Present age of Ram = 10 years.

For first case :-

5 years ago, Ram's mother was five times his age

Present age of Ram = 10 years

5 years ago,

Ram's age = 10 - 5 = 5 years

Present age of Mother = 30 years

5 years ago,

Mother's age = 30 - 5 = 25 years

Let's check if the ages satisfies the first condition,

Mother's age = 5 ( Ram's age )

25 = 5 ( 5 )

25 = 25

LHS = RHS.

For second case :-

His mother is now thrice as old as him

Mother's age = 30 years

Ram's age = 10 years

Let's check whether the second condition is satisfied or not.

Mother = 3 ( Ram's age)

30 = 3 ( 10)

30 = 30

LHS = RHS.

Hence the answer is verified.