Question

the brother is elder to his sister by 6 years. seven years ago the product of their ages was 72. what is the age of brother​

Answer 1

☯GIVEN :

• The brother is elder to his sister by 6 years.

• Seven years ago, the product of brother's age and sister's age was 72.

☯TO FIND :

• The Present Age Of Brother.

➲SOLUTION :

Let the present age of sister be x years.

• Then, the present age of brother = (x+6) years

Seven Years Ago,

• The age of sister = (x-7) years

• The age of brother = (x+6-7) = (x-1) years

✞We know that,

• Seven years ago, the product of brother's age and sister's age was 72.

★ According to the question :

$\longmapsto \sf{Brother's \: age \times Sister's\: age = 72}$

$\longmapsto \sf{(x - 1) (x -7) = 72 }$

$\longmapsto \sf{x(x - 1) - 7(x -1)= 72 }$

$\longmapsto \sf{ x^2- x- 7x + 7 = 72}$

$\longmapsto \sf{ x^2- 8x + 7 = 72}$

• Transposing 72 to LHS by changing its sign.

$\longmapsto \sf{ x^2- 8x + 7 - 72=0}$

$\longmapsto \sf{ x^2- 8x - 65=0}$

$\longmapsto \sf{ x^2 + 5x -13x - 65=0}$

• Middle term splitting.

$\longmapsto\sf{ x(x + 5) -13(x + 5 )=0}$

$\longmapsto\sf{ (x + 5) (x - 13 )=0}$

$\longmapsto\sf{ (x + 5) = 0 \: , \: (x - 13 )=0}$

$\longmapsto\sf{ x = 0 - 5\: , \: x =0 + 13}$

$\longmapsto\bf{ x = - 5\: , \: x = 13}$

• Age can't be negative.

★The Present Age Of Sister :

• x years = 13 years

★The Present Age of Brother :

• (x+6) years = 13+6 = 19 years

• ✞ Final Answer :

$\huge{\blue{\therefore}}$ The Present Age Of Brother is 19 years.