Question

12. A mother said to her son, 'the sum of our present
ages is twice my age 12 years ago and nine years
hence, the sum of our ages will be thrice my age 14
years ago? What is her son's present age? (in years)
​

Answer 1

Heya!

Here is UR ANSWER ..

Let the present age of the son is x years

The present age of the mother is y years

According to the Hypothesis..

The sum of the present age of mother and son is twice the age of mother 12 years ago

The age of mother 12 years ago is = (y-12)

Therefore,

x+y = 2(y-2)

x+y = 2y-4

x+y-2y = -4

x-y = -4 .......... (1)

And,

Nine years ago sum of the ages of the mother and son is thrice the age of mother..14 years ago

9 years ago,

age of the son = (x-9)years

age of the mother =(y-9)years

Therefore,

(x-9)+(y-9)= 3 (y-14)

x-9+y-9 = 3y-42

x-2y=-42 .............. (2)

From (1) and (2),

x-y = -14

x-2y= -42

- + +

__________

y = 28

By sub. y = 28 in equation (1),

x-28 = -4

x = -4+28

x = 24