Question

Mary told her daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." Find the present age of Mary and her daughter.

Answer 1

Let present age of her daughter is x yrs
and present age of Mary is y yrs.

a/c to question,
seven yrs ago, Mary was seven times old as her daughter .
e.g., (y - 7) = 7(x - 7)
y - 7 = 7x - 49
y = 7x - 42 .............(i),

again, three yrs from now , Mary will be three times as old as her daughter will be.
e.g., (y + 3) = 3(x + 3)
y + 3 = 3x + 9
y = 3x + 6 ........(ii),

solving equations (i) and (ii),
=> 7x - 42 = 3x + 6
=> 7x - 3x = 6 + 42
=> 4x = 48
=> x = 12
and y = 3 × 12 + 6 = 42

hence, present age of Mary = 42 yrs
present age of her daughter = 12 yrs

Answer 2

SOLUTION : Let present age of mother (Mary) be x yr and the  present age of daughter be y yr. 7 yr (Seven year) ago : Mary’'s age  = (x - 7) yr daughter’s = (y - 7) yr A T.Q, (x - 7)  = 7 (y – 7 ) x – 7 = 7y – 49 x- 7y = - 49 + 7  x - 7y = - 42 ………….(1) After 3 yr : Mary’'s age  = (x +3) yr daughter’s = (y +3) yr A T.Q, (x + 3) = 3 (y + 3) x + 3 = 3y + 9 x - 3y = 9-3 x - 3y = 6 x = 3y + 6 ………….(2) On Putting the value of x in eq 1 x - 7y = - 42 3y + 6 - 7y = - 42 3y -7y = - 42 - 6 -4y  = -48 y = 48/4 = 12 y = 12 yr  On Putting y = 12 in eq 2 x = 3y + 6 x = 3(12) + 6 x = 36 + 6 = 42  x = 42 yr  Hence, the the present age of Mary is 42 yr and her daughter age is 12 yr.  HOPE THIS ANSWER WILL HELP YOU….