Question

# 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?

Hint:

### let present ages of son is x years and present age of mom is y years

Add their present ages and equate it to twice the age of mother 12 years ago.

Calculate their ages After 9 years and apply the condition the sum of our ages will be thrice my age 14 years ago .

## The correct answer is: 12 years

### Ans :- present age of son is 12 years

Explanation :-

Step 1:- find the equation by 1st condition.

let present ages of son is x years and present age of mom is y years

The sum of our present ages is twice my age 12 years ago.

x + y =2( y-12) [ the age of 12 years ago is present age -12 years]

— Eq1

Step 2:- find the equation by applying second condition

After 9 years the sons age = x+9

After 9 years the mothers age = y+9

Mother age 14 years ago = present age - 14 years = y - 14

After 9 years ,the sum of our ages will be thrice my age 14 years ago

— Eq2

Step 3:- find value of x by eliminating y

Doing 2(Eq1)-Eq2 to eliminate y

∴ present age of son = x= 12 years.

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