Question

four years ago a father was nine times as old his son,and 8 year hence the father's will be three times the son's age.find their present age.​

Answer 1

Four years ago a father was nine times as old his son.

Let the -

• present age of father be M years.
• present age of son be N years.

According to question,

=> M - 4 = 9(N - 4)

=> M - 4 = 9N - 36

=> M = 9N - 36 + 4

=> M = 9N - 32 _____ (eq 1)

Also,

8 year hence the father's will be three times the son's age.

According to question,

=> M + 8 = 3(N + 8)

=> M + 8 = 3N + 24

=> 9N - 32 + 8 = 3N + 24 [From (eq 1)]

=> 9N - 24 = 3N + 24

=> 9N - 3N = 24 + 24

=> 6N = 48

=> N = 8

Substitute value of N in (eq 1)

=> M = 9(8) - 32

=> M = 72 - 32

=> M = 40

•°• Present age of father is 40 years.

Present age of son is 8 years.

Answer 2

ANSWER:-

Given:

Four years ago, a father was 9 times as old his son & 8 years hence the father's will be three times the son's age.

To find:

The present age of father & son.

Solution:

Let the father's age be R &

Let the son's age be M.

Therefore,

•Four years ago:

Father's age= R-4

Son's age = M-4

So,

=) R-4= 9(M-4)

=) R- 4= 9M -36

=) R -9M= -36+4

=) R - 9M= -32.................(1)

&

•Eight years hence:

Father's age= R+8

Son's age= M+8

So,

=) R+8= 3(M+8)

=) R+8= 3M + 24

=) R - 3M= 24 -8

=) R - 3M=16.................(2)

Now,

Substitution Method:

From equation (1), we get,

=) R - 9M= -32

=) R= -32+9M.................(3)

So,

Putting the value of R in equation (2), we get;

=) -32 + 9M -3M= 16

=) -32 + 6M= 16

=) 6M= 16 +32

=) 6M= 48

=) M= 48/6

=) M= 8 years

&

Putting the value of M in equation (3), we get;

=) R= -32 + 9(8)

=) R= -32 + 72

=) R= 40 years

Thus,

The present age's of father,R= 40 years.

&

The present age's of son, M= 8 years.

Hope it helps ☺️