Question

The sum of father’s 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

Given :-

The sum of father’s age and twice the age of his son is 70.

When we double the age of  father and add it to the age of his son, the sum is 95.

To Find :-

The present age of father.

The present age of son.

Analysis :-

Consider both of their ages as variables.

Make equations in 2 cases according to the situation given in the question.

Then find the value of the two variables accordingly.

Solution :-

Let the father's and the son's age be 'x' and 'y' respectively.

When the sum of fathers age and twice the age of his son is 70,

Making the equation,

$\sf x+2y=70$

$\sf x=70-2y \quad ....(1)$

While doubling the age of the father and adding it to the son’s age sum is 95,

$\sf 2x+ y= 95 \quad ....(2)$

Multiplying equation (1),

$\sf 2x+4y=140 \quad ....(3)$

Subtracting equation (2) from (3),

$\sf 3y=45$

$\sf y=\dfrac{45}{3}$

$\sf y=15$

Therefore, the age of son is 15 years.

Substituting the value of y in equation (2),

$\sf 2x+15=95$

Transposing 15,

$\sf 2x=95-15$

$\sf 2x=80$

Finding the value of x,

$\sf x=\dfrac{80}{2}$

$\sf x=40$

Age of father = 40 years

Therefore, the ages of father and son is 40 and 15 years respectively.

Answer 2

Answer:

Given:-

• 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 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 2Y + Y = 95 .

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

2(70 –2Y ) + Y = 95

140 – 4 Y + Y =95

y=15

substitute Y =15 in X 70 – 2Y ,we get X= 40

Step-by-step explanation:

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