Question

Three years ago A's age was double of B's age. Seven years hence, the sum of their ages will be 83 years.Find the present age of each.
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Answer 1

Given:

• Three years ago A's age was double of age of B.
• After seven years ,the sum of their ages will be 83 years.

To Find:

• The present ages of A and B.

Answer:

Given that three years ago A's age was double of B's age .

And ,after seven years the sum of their ages will be 83 years.

Let → Present age of A be x .

→ Present age of B be y .

$\rule{200}4$

Case 1: Three years ago .

• Age of A = ( x - 3 ) .
• Age of B = ( y - 3 ).

Atq ,

$\sf{\implies x - 3 =2(y-3)}$

$\sf{\implies x - 3 = 2y - 6}$

$\sf{\implies x - 2y = 3 -6}$

$\boxed{\red{\bf{\leadsto x - 2y=-3}}}$ ............(1)

$\rule{200}4$

Case 2: After 3 years .

• Age of A = (x +3).
• Age of B = (y + 3).

Atq ,

$\sf{\implies (x + 7 )+ (y +7)=83}$

$\sf{\implies x + 7 + y +7=83}$

$\sf{\implies x + y +14=83}$

$\sf{\implies x + y =83-14}$

$\boxed{\red{\bf{\leadsto x + y = 69}}}$ ..........(2)

$\rule{200}4$

Now , $\sf{\hookrightarrow equ^{n}1-equ^{n}2}$

$\rm{\implies x - 2y = -3 }$

—$\sf{\:\:\:\cancel{ x} \pm y = -69 }$

_______________________

$\sf{\implies -3y = -72}$

$\sf{\implies y=\cancel{\dfrac{-72}{-3}}}$

${\underline{\boxed{\red{\sf{\longmapsto y=24}}}}}$

Hence value of y is 24.

Putting this value in ② ,

$\sf{\implies x + y=69}$

$\sf{\implies x + 24=69}$

$\sf{\implies x =69-24}$

${\underline{\boxed{\red{\sf{\longmapsto x=45}}}}}$

Hence present

• Age of A = x = 45years.
• Age of B = y = 24years