Question

the sum of the ages of father and son is 42 and after 4 years the father's age will be four times the age of the son so find their present ages​

Answer 1

The present age of the father and the son :

• The present age of the father = 36 years.
• The present age of the son = 6 years.

Given :

• The sum of the ages of father and son = 42 years.
• After 4 years, the age of father will be four times the age of the son.

To Find :

• The present age of father and son.

Solution :

Let,

The age of the father be x.

The age of the son be y.

Given,

The sum of their age is 42 years.

That means,

$: \implies \rm x + y = 42 \\ \\ : \implies \rm y = 42 - x \: \: \: \: \: ........(1)$

After four years,

The age of the father = x + 4.

The age of the son = y + 4.

According to the question,

The age of the father will be four times the age of the son.

That means,

$: \implies \rm x + 4 = 4(y + 4) \: \: \: \: \: ........(2)$

Substitute the equation (1) in the equation (2),

$: \implies \rm x + 4 = 4\bigg((42 - x) + 4 \bigg) \\ \\ : \implies \rm x + 4 = 4(42 - x + 4) \\ \\ : \implies \rm x + 4 = 4(42 + 4 - x) \\ \\ : \implies \rm x + 4 = 4(46 - x) \\ \\ : \implies \rm x + 4 =184 - 4x \\ \\ : \implies \rm x + 4x = 184 - 4 \\ \\ : \implies \rm 5x = 180 \\ \\ : \implies \rm x =\dfrac{180}{5} \\ \\ : \implies \rm x = 36 \\ \\ \: \: \rm \therefore \: \: x = 36$

Hence, the present age of the father is 36 years.

Now, we have to find the age of the son.

Substitute the value of x in the equation (1),

$: \implies \rm y = 42 - x \\ \\ : \implies \rm y = 42 - 36 \\ \\ : \implies \rm y = 6 \\ \\ \: \: \rm \therefore \: \: y = 6$

Hence, the present age of the son is 6 years.

Hence,

The present age of the father and the son is 36 years and 6 years.

Verification :

Method 1 :

The sum of their ages is 42 years.

$: \implies \rm x + y = 42 \\ \\ \sf we \: have \\ \: \: \orange\bullet \tt \: \: \: x = 36 \\ \: \: \orange \bullet \tt \: \: \: y = 6 \\ \\ : \implies \rm 36 + 6 = 42 \\ \\ : \implies \rm 42 = 42$

Hence Verified !

Method 2 :

The age of the father will be four times the age of the son.

From the equation (2),

$: \implies \rm x + 4 = 4(y + 4)\\ \\ \sf we \: have \\ \: \: \orange\bullet \tt \: \: \: x = 36 \\ \: \: \orange \bullet \tt \: \: \: y = 6 \\ \\ : \implies \rm 36 + 4 = 4(6 + 4) \\ \\ : \implies \rm 40 = 4(10) \\ \\ : \implies \rm 40 = 4 \times 10 \\ \\ : \implies \rm 40 = 40$

Hence Verified !

Answer 2

Answer:

Let Father's age be x

and son's age be y

x+v=42

y=42-n

After 4 years

4(x+4)=(y+4)

4x+6=y+4

4x-y=-12

4x-(42-x) =-12

4x+x=42-12

5x=30

x=6

y=42-6=36

so, after 4 years the son's age is 10

and father's age is 40

Step-by-step explanation:

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