Question

The sum of fathers age and twice the age of his son is 70. If we double the age of father and add it to the age of his son the sum is 95. Find their present ages.

Answer 1

Father’s present age:  40.

Son’s present age: 15.

Solution:

Let us take the father‘s age as “X” and son’s age as “Y”.

Now as given in question the sum of father’s age and twice the son’s age,

X + 2Y = 70 _______ (1)

As per given data, doubling the age of the father and adding it to the son’s age sum is 95,

2X + Y = 95 _______ (2)

Hence to find their present age of X and Y, we equate

(X + 2Y) = 70 and 2X + Y = 95.

To solve (2) equation, substitute X = 70 – 2Y in X of 2X + Y =95, 

2(70 – 2Y) + Y = 95

140 – 4Y + Y = 95

Y = 15

Substitute Y = 15 in X = 70 – 2Y, we get  

X = 40

Answer 2

Answer:

$Father's\:age=40\:years\\age\:son's\:age = 15 \:years$

Step-by-step explanation:

$Let\: Father's\:age=x\:years\\age\:son's\:age = y \:years$

The sum of fathers age and twice the age of his son is 70.

$x+2y=70\\\implies x=70-2y---(1)$

double the age of father and add it to the age of his son the sum is 95

$2x+y=95---(2)$

Substitute x=70-2y in equation (2),we get

$\implies 2(70-2y)+y=95$

$\implies 140-4y+y=95$

$\implies -3y=95-140$

$\implies -3y = -45$

$\implies y =\frac{-45}{-3}$

$\implies y = 15$

Now, put y=15 in equation (1),we get

$x = 70-2\times 15$

$\implies x = 70 - 30$

$\implies x = 40$

Therefore,

$Father's\:age=40\:years\\age\:son's\:age = 15 \:years$