Question

When the son will be as old as his father today the sum of their ages then will be 126 when the father was as old as is son today the sum of their ages was 38 find their present age?

Answer 1

Answer:

_______________________________

Let the present age of father be x years.

Let the present age of son be y years.

Also,

Son's age when he will be as old as his father today= x years.

Therefore,

Father's age at that time

=[x+(x-y) ] years.

According to the first condition,

x+x+(x-y)=126

3x-y=126.------>1

Father's age will when he was as old as his son =y years.

Therefore,

son's age at that time,

=[y-(x-y)]years

According to the second condition,

y+y-(x-y)=38

y+y-x+y=38

-x+3y=38----->2

Multiying eq.2 by 3

-3x+9y=114----->3

Adding eq.1 and eq.3 we get,

$\\ \: \: \: \: \: \: \: \: \: 3x - y = 126 \\ \: \: - \: \: \: 3x + 9=114 \\ - - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 8y = 240$

Therefore,

$\\ = > y = \frac{240}{8} \\ \\ = > y = 30$

Substituting the above value of y in eq.1 we get,

3x-30=126

3x=126+30

3x=156

$\\ = > x = \frac{156}{3} \\ \\ = > x = 52$

Therefore,

the present age of father is x=52yrs.

&

The present age of son y=30yrs.

Answer 2

Solutions :-

Let the son's age be x
And father's age be y

Given : When the son will be as old as his father today the sum of their ages then will be 126.

=> [y+(y-x)] + [(x + (y-x))] = 126
=> 2y - x + y = 126
=> 3y - x = 126 _______(i)

Given : When the father was as old as his son today the sum of their ages was 38.

=> [y - (y-x)] + [x - (y-x)] = 38
=> x + x - y + x = 38
=> 3x - y = 38
=> y = 3x - 38 _______(ii)

Putting the value of y in equation (i) we get,

=> 3(3x - 38) - x = 126
=> 9x - 114 - x = 126
=> 8x = 126 + 114
=> 8x = 240
=> x = 240/8 = 30

Now,
Putting the value of x in equation (ii) we get,

=> y = 3(30) - 38
=> y = 90 - 38 = 52

Hence,
Present age of Son = 30 years
Present age of father = 52 years