Question

Aftab tells his 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 find the present age of aftab& his daughter (x &y). (Hint: Aftab age is x & daughter age is y) ​

Answer 1

Solution :-

Let :-

Present age of Aftab = x

Present age of daughter = y

Seven years ago :-

Age of Aftab = x - 7

Age of daughter = y - 7

After three years :-

Age of Aftab = x + 3

Age of daughter = y + 3

According to the first condition :-

$\longrightarrow \sf x-7 = 7(y-7) \\\\\longrightarrow x-7 = 7y - 49 \\\\\longrightarrow x-7y = -42 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............................(1)$

According to the second condition :-

$\longrightarrow \sf x+3 = 3(y+3) \\\\\longrightarrow x+3 = 3y + 9 \\\\\longrightarrow x-3y = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............................(2)$

Equation (2) - Equation (1) :-

$\longrightarrow \sf 4y = 48 \\\\\longrightarrow \bf y = 12$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf x- 12 \times 3 = 6 \\\\\longrightarrow x - 36 = 6 \\\\\longrightarrow \bf x= 42$

Present age of Aftab = 42 years

Present age of daughter = 12 years

Answer 2

Step-by-step explanation:

Let

the present age of Aftab=x

the present age of daughter=y

Seven years ago :-

the age of father=x-7

the age of daughter=y-7

After 3 years :-

the age of father=x+3

the age of daughter=y+3

According to the first condition,

${:}\longrightarrow$$x-7=7(y-7)$

${:}\longrightarrow$$x-7=7y-49$

${:}\longrightarrow$$x-7y=-49+7$

${:}\longrightarrow$$x-7y=-42...........(1)$

According to the second condition:-

${:}\longrightarrow$$x+3=3 (y+3)$

${:}\longrightarrow$$x+3=3y+9$

${:}\longrightarrow$$x-3y=9-3$

${:}\longrightarrow$$x-3y=6............(2)$

Equation(2)-Equation(1):-

${:}\longrightarrow$$4y=48$

${:}\longrightarrow$$y={\frac{48}{4}}$

${:}\longrightarrow$${\underline{\boxed {\bf{y=12}}}}$

Substitute the value of y in Equation(1):-

${:}\longrightarrow$$x-7×12=-42$

${:}\longrightarrow$$x-84=-42$

${:}\longrightarrow$$x=-42+84$

${:}\longrightarrow$${\underline{\boxed {\bf{x=42}}}}$

$Present\: age\: of\:Aftab {}_{(x)}=42years$

$Present\:age\:of\:daughter{}_{(y)}=12years$