Question

Five years ago, a mother was seven times as old as her daughter. five years hence, she will be three time as old as her daughter. Find their present age.

Answer 1

ANSWER


LEt mother = M and Daughter = D
M - 5 = 7(D -5)
M = 7D - 30 …….1
M + 5 = 3 (D + 5)
M = 3D + 10 …..2
equate 1 & 2
3D + 10 = 7D - 30
4D = 40
D = 10 daughter is 10


so them mother = 3D + 10 = 40
mother is 40 and daughter = 10



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Answer 2

$\textsf{Let the Present Age of the Daughter be : D}$

$\textsf{Let the Present Age of her Mother be : M}$

$\underline{\textsf{Five Years ago :}}$

$\bigstar \;\;\textsf{The Age of Daughter will be : D - 5}$

$\bigstar \;\;\textsf{The Age of Mother will be : M - 5}$

$\textsf{Given : Five years ago, The Mother was Seven times as old as her Daughter}$

$\sf{\implies M - 5 = 7(D - 5)}$

$\sf{\implies M - 5 = 7D - 35}$

$\sf{\implies 7D - M = 30\;------\;[1]}$

$\underline{\textsf{Five Years hence :}}$

$\bigstar \;\;\textsf{The Age of Daughter will be : D + 5}$

$\bigstar \;\;\textsf{The Age of Mother will be : M + 5}$

$\textsf{Given : Five years hence, The Mother was Three times as old as her Daughter}$

$\sf{\implies M + 5 = 3(D + 5)}$

$\sf{\implies M + 5 = 3D + 15}$

$\sf{\implies 3D - M = -10\;-------\;[2]}$

$\textsf{Subtracting Equation [2] from Equation [1], We get :}$

$\sf{\implies (7D - M) - (3D - M) = 30 + 10}$

$\sf{\implies 7D - M - 3D + M = 40}$

$\sf{\implies 4D = 40}$

$\sf{\implies D = 10}$

$\textsf{Substituting D = 10 in Equation [1], We get :}$

$\sf{\implies 7(10) - M = 30}$

$\sf{\implies M = 70 - 30}$

$\sf{\implies M = 40}$

$\underline{\sf{Answers :}}$

$\bigstar\;\;\textsf{The Present Age of Daughter = 10\;Years}$

$\bigstar\;\;\textsf{The Present Age of her Mother = 40\;Years}$