Question

Sum of the ages of father and his daughter is 70 years. After 10 years father will be twice as old as his daughter. Find their present ages.​

Answer 1

Answer:-

• Age of father is 50 years.

• Age of daughter is 20 years.

Explanation:-

Given:-

• Sum of ages of father and daughter = 70

• After 10 years fathers age is twice as old as daughter.

To Find:-

• The present ages of father and daughter.

Solution:-

Let the ages of father and daughter be x and y respectively.

So ATQ:-

$\\ \tt \mapsto x + y = 70...eq(1).$

After 10 years:-

• Age of father = 10+x.
• Age of daughter = 10+y.

$\\ \tt \mapsto(10 + x) = 2(10 + y).$

$\\ \tt \mapsto10 + x = 20 + 2y.$

$\\ \tt \mapsto x - 2y = 20 - 10.$

$\\ \tt \mapsto x - 2y = 10...eq(2).$

Subtracting eq(2) from eq(1),

$\\ \tt \mapsto(x + y) - (x - 2y) = 70 - 10.$

$\\ \tt \mapsto \cancel{x} + y \cancel{ - x} + 2y = 60.$

$\\ \tt \mapsto3y = 60.$

$\\ \tt \mapsto y = \cancel \frac{60}{3} .$

$\\ \large\bf \mapsto \boxed{ \bf y = 20.}$

Therefore The Present age of daughter is 20 years.

By putting the value of y in eq(1) :-

$\\ \tt \mapsto x + y = 70.$

$\\ \tt \mapsto x = 70 - 20.$

$\\ \large\tt \mapsto \boxed{ \bf x = 50.}$

Therefore The Age of Father is 50 years.

And Hence the ages of the father and daughter are 50 and 20 years respectively.

Answer 2

Given :-

Sum of the ages of father and his daughter is 70 years. After 10 years father will be twice as old as his daughter

To Find :-

Present ages

Solution :-

Let the age of daughter be x

age of father = 70 - x

After 10 years

Sum of ages = 90

Age of daughter =  x + 10

Age of father = 2(x + 10)

x + 10 + 2(x + 10) = 90

x + 10 + 2x + 20 = 90

3x + 30 = 90

3x = 90 - 30

3x = 60

x = 60/3

x = 20

Age of father = 70 - 20 = 5-0 years