Question

Q6.Sum of the ages of father and his son is 60 years. After 14 years, father's age will be three
times the age of the son Find the present ages
(3)​

Answer 1

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Q) Sum of the ages of father and his son is 60 years . After 14 years , father's age will be three times the age of the son . Find their present ages .

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★ Given :

• Sum of ages of father and son is 60 years .
• After 14 yrs , father's age would be 3 times the son's age .

★ To Find :

• The present ages of the father and the son .

★ Solution :

Let the present age of son be x years .

$\sf \: sons \: age + fathers \: age = 60$

$\sf \: x \: + fathers \: age = 60$

Present age of father = 60-x years .

Now ,

After 14 years ,

• Age of Son = x + 14 yrs
• Age of father = 60-x+14 = 74 - x yrs

According to the Question ,

$\rm \: age \: of \: father = 3 \times age \: of \: son$

$\mapsto \rm \: 74 - x = 3(x + 14)$

$\mapsto \rm \: 74 - x = 3x + 42$

$\mapsto \rm \: 3x + x = 74 - 42$

$\mapsto \rm \: \cancel4x = \cancel{32}$

$\mapsto \boxed{ \red{\rm \: x = 8}}$

So ,

• Present age of Son = 8 years
• Present age of father = 60-8 = 52 years

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Answer 2

The age of father is 52

The age of son is 8

Given :

Sum of ages of father and son is 60

After 14 years age of father is thrice the age of son

To Find :

find present Age of son and father

Formation of equation :

Let ,

present age of father as x

present age of son as y

As by given , the sum of son's age and father age is 60. hence,

$x+y=60........(1)$

And after 14 years, the age of father is thrice the age of son. hence,

$x+14=3(y+14)$

$x+14 = 3y+42$

$x-3y=42-14$

$x-3y = 28......(2)$

Solution :

$x+y = 60$

$x-3y=28$

Shall use elimination method,

$x+y=60\\x-3y=28\:\:\:(-)\\------\\4y = 32\\y=\frac{32}{4} \\ \implies y = 8$

Substitute the value of y in (1)

$\implies x+y=60$

$\implies x+8=60$

$\implies x=60- 8$

$\implies x = 52$

Verification :

Substitute the value of x and y in the equations,

Substitute values in (1)

$\implies x+y=60\\ \implies 52+8 = 60 \\ \implies 60 = 60$

Substitute values in (2)

$\implies x+14=3(y+14)\\ \implies 52+14 = 3(8+14) \\ \implies 66 = 3(22) \\ \implies 66 = 66$

Hence verified.