Question

five years ago, the ratio of the ages of a mother and her daughter was 7:2. After 10 years, the ages of the daughter will be half the age of her mother. what is the present age of the mother?

Answer 1

Let the mother's age be 7x and her daughter's be 2x (5 years ago)

after 10 years from present

(7x+15)/2 = 2x+15
7x+15 =4x+30
3x = 15

x=5

Their present ages are

Mom =7*5+5 =40
daughter = 2*5+5 =15  

Answer 2

$\underline{\textbf{Hey Mate Here is Your Answer }}$

$\underline{\textbf{Given That..}}$

5 Years Ago The Ratio Of The Age Of Mother And Her daughter is 7:2 And It's Said That After 10 years The

Age Of Daughter Will Be Half Of The Age Of The Mother , Now We Need To Find Present Age Of Mother ..

So Now Let's Move For Solution..

$\underline{\textbf{Solution..}}$

So To Find The Present Age Of Mother Follow The Simple Steps..

$\underline{\bold{Step - 1 ) D efi ne \:All\: Required \:Terms \:With \:Help \:of \:Variables}}$

Now According To Question 5years Ago The Ratio of The Mother's Age To Daughter Is 7:2

$\textbf{Now Let " X " Be The Constant Of Ratio }$

Therefore Age Of

$\textbf{Mother's Age before 5 years Would Be = 7x}$

And Similarly

$\textbf{Daughter's Age Before 5 years Would Be = 2x}$

So Present Age Of

$\textbf{Mother Would Be = 7x + 5 }$

And

$\textbf{ Daughter Would Be = 2x + 5 }$

And

Now Age of

$\textbf{Mother after 10 years Would Be = 7x + 5 + 10 }$

That Is $\boxed{\bold{7x \:+ \:15 }}$

And Similarly Age Of

$\textbf{Daughter after 10 years Would Be = 2x + 5 + 10 }$

That Is $\boxed{\bold{2x \:+ \:15 }}$

$\underline{\textbf{Step -2 ) Form An Equation With The Help Of Given Information }}$

Now According To Question It's Said That ..

After 10 Years Age Of Daughter Would Be Equal To Half The Age Of Mother ..

So We Have

$\textbf{Daughter's Age After 10 year = 1/2 Mother's Age after 10 year}$

That Is ..

$\boxed{\mathbf{2x + 15 = \frac{1}{2} ( 7x + 15) }}$

$\underline{\textbf{Step -3 ) Solve The Obtained Equation}}$

$\mathbf{2x + 15 = \frac{1}{2}\: ( 7x + 15) }$

Now Taking 1/2 To LHS We Have

$\mathbf{2(2x + 15) = ( 7x + 15) }$

Now Opening Brackets We Have..

$\mathbf{4x + 30 = 7x + 15 }$

Now Taking 30 To RHS And 7x to LHS We Have..

$\mathbf{4x - 7x = 15 - 30}$

So That Is

$\mathbf{ - 3x = - 15 }$

Now Taking -3 To RHS We Have..

$\mathbf{x = ( - 15 )\div ( - 3)}$

Therefore We Have Value Of

$\boxed{ \mathbf{x = 5}}$

$\underline{\textbf{Step - 4 ) Put The Obtained Value Of X In The Present Age Mother And Daughter }}$

Now We Have Value Of $\mathbf{X\: =\: 5}$

Now We Know That

$\textbf{ Present Age Of Mother = 7x + 5 }$

And

$\textbf{ Present Age Of Daughter = 2x + 5 }$

Now Putting Value Of X = 5 In Their Present Ages We Have ..

$\mathbf{ Present \:Age\: Of \:Mother \:= \:7x\: +\: 5\Longrightarrow \:7\times 5 \:+\: 5\: = \:\boxed{\mathbf{40years}}}$

And

$\mathbf{ Present\: Age\: Of \:Daughter \:=\: 2x\: +\: 5\Longrightarrow \:2\times5 \:+ \:5 \:= \boxed{\mathbf{15years}}}$

$\underline{\textbf{Hence The Required Answer Is }}$

$\boxed{\boxed{\mathbf{ 40\: Years}}}$

$\mathfrak{\bold{Thanks..}}$