Question

8 years ago the age of the father was four times that of his son. 12 years hence the age of the Son will be two third of the of his father. what are their present age​

Answer 1

Answer:

yes

Step-by-step explanation:

Consider the present age of the son as 'x' and the father's age as 'y'.....

In the first case:

Since, it is 8 years before

4(x-8)=y-8     [4 times of son's age is father's age]

4x-32=y-8

4x-y=24                        .......(i)

In the second case:

Now it is 12 years after

(x+12)=(2/3)(y+12)

3(x+12)=2(y+12)

3x+36=2y+24

3x-2y=-12                     ........(ii)

From (i) and (ii):

Multiply (i) by 2

8x-2y=48                    [From (i)]

3x-2y=-12                    [From (ii)]

Solving the both eqns, we get:

x=12;y=24

Therefore, the present ages of son and the father are 12 and 24 respectively....

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Answer 2

Answer:

Son's age = 12

Father's age = 24

Step-by-step explanation:

Let the present age of the son be = x

And that of his father be = y

According to the question,

$4(x - 8) = (y - 8)$

Because 8 years ago would mean in the past and present age minus 8

And in the second case

$(x + 12) = \frac{2(y + 12)}{3}$

Because 12 years hence would mean in the future and present age plus 12

Now rearranging these two equations we will get -

$4x - 32 = y - 8 \\ 4x - y = 24$

Similarly

$3(x + 12) = 2(y + 12) \\ 3x + 36 = 2y + 24 \\ 2y - 3x = 12$

Now if we solve the 3rd equation for y we get -

$y = 4x - 24$

Now using substitution we put this value of y in equation 4

$2(4x - 24) - 3x = 12 \\ solving \: this \\ 8x - 48 - 3x = 12 \\ 5x = 48 + 12 \\ x = \frac{60}{5} = 12$

Now using X = 12 in the 5th equation,

$y = 4(12) - 24 \\ y = 48 - 24 \\ y = 24$