Question

Ten years ago a father was six times as old as his daughter. After 10 years, he will be twice as old as his daughter. Determine their present ages.

Answer 1

Hii friend,

Let the present age of father and daughter be X and Y year's.

Before 10 years age of father = (X-10) years.

Before 10 years age of daughter = (Y-10) years.

According to question,

(X-10) = 6(Y-10)

X-10 = 6Y - 60

X-6Y = -60+10

X-6Y = -50......(1)

After 10 years age of father = (X+10) years.

After 10 years age of daughter = (Y+10) years.

According to question,

X+10 = 2(Y+10)

X+10 = 2Y + 20

X-2Y = 20-10

X -2Y = 10.....(2)

From equation 1 we get,

X-6Y = -50

X = -50+6Y,....(3)

Putting the value of X in equation (2)

X -2Y = 10

(-50+6Y) -2Y = 10

-50+4Y = 10

4Y = 10+50

4Y = 60

Y = 60/4

Y = 15.

Putting the value of Y in equation (3)

X = -50+6Y

X = -50 + 6 × 15

X = -50+90 = 40 years

Age of daughter = Y = 15 years.

Age of father = X = 40 years.

HOPE IT WILL HELP YOU..... :-)

Answer 2

Hello dear friend .
Here is Ur answer .
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Let the present age of father = x
and present age of his daughter = y

Ten years ago
father's age = (x - 10)
and his daughter age = (y - 10)

Given that father was six times as old as his daughter.
$= > x - 10 = 6(y - 10) \\ = > x - 10 = 6y - 60 \\ = > x - 6y = - 60 + 10 \\ = > x - 6y = - 50 \: \: \: \: \: \: \: \: \: \: \: \: ...........(1)$
Ten years later
father's age = (x+10) years
and daughter's age = (y+10) years

given that father will be twice as old as his daughter.
$= > x + 10 = 2(y + 10) \\ = > x + 10 = 2y + 2(10) \\ = > x + 10 = 2y + 20 \\ = > x - 2y = 20 - 10 \\ = > x - 2y = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: .........(2)$
Hence our equation are -
x- 6y = -50 ........(1)
x-2y = 10 ........(2)

using elimination method with equation (1) and (2)

$\: \: \: \: \: \: \: \: \: \: \: \: x - 6y = - 50 \\ \: \: \: \: \: \: \: \: \: \: \: \: x - 2y = 10 \\ \: \: \: \: \: \: \: ( - ) \: \: \: \: ( + ) \: \: \: ( - ) \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \:= = = = = = = = = = = = \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4y = 60$
4y = 60
y = 60/4 = 15
y = 15

putting y = 15 in equation (1)
$= > x - 6y = - 50 \\ = > x - 6(15) = - 50 \\ = > x - 90 = - 50 \\ = > x = - 50 + 90 \\ = > x = 40$
so, the present age of father is x = 40 years
and his daughter's age is y = 15 years .

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Hope it's helps you.
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