Maths-
General
Easy

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?

hintHint:

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]
    not stretchy rightwards double arrow x plus y equals 2 y minus 24 not stretchy rightwards double arrow x minus y equals negative 24 — 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
    left parenthesis x plus 9 right parenthesis plus left parenthesis y plus 9 right parenthesis equals 3 left parenthesis y minus 14 right parenthesis
    not stretchy rightwards double arrow x plus y plus 18 equals 3 y minus 42
    not stretchy rightwards double arrow x minus 2 y equals negative 60— Eq2
    Step 3:- find value of x by eliminating y
    Doing 2(Eq1)-Eq2 to eliminate y
    not stretchy rightwards double arrow 2 left parenthesis x minus y right parenthesis minus left parenthesis x minus 2 y right parenthesis equals 2 left parenthesis negative 24 right parenthesis minus left parenthesis negative 60 right parenthesis
    not stretchy rightwards double arrow 2 left parenthesis x minus y right parenthesis minus left parenthesis x minus 2 y right parenthesis equals 2 left parenthesis negative 24 right parenthesis minus left parenthesis negative 60 right parenthesis
    therefore space x space equals space 12
    ∴ present age of son = x= 12 years.

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