Question

26) A boy's age is one-fourth that of his father. After
24 years the boy will be half the age of his father.
Find their present ages.​

Answer 1

Answer:

Boy age at present=x/4

Present age of father=x

By the given data

x/4+24=x+24/2

[96+x/4]2=x+24

96+x=2(x+24)

96-48=2x-x

x=48

Present age of father =x=48 years

Present age of the boy = x/4=48/4=12 years

Hope it helps u...

Answer 2

Answer :

The present age of the boy is 12 years, and his Father age is 48 years.

Step-by-step explanation :

Let the boy's age be $\sf{ \dfrac{x}{4}}$ years and the father's age be x years.

Given that, After 24 years, the boy will be half the age of his father.

Therefore,

Age of father, after 24 years = $\sf{ \dfrac{x + 24}{2}}$

And age of boy, after 24 years = $\sf{ \dfrac{x}{4}} + 24$

$\sf{ \longrightarrow \: \dfrac{x + 24}{2} = \dfrac{x}{4} + 24}$

$\sf{ \longrightarrow \: \dfrac{1}{2}x + 12 = \dfrac{1}{4}x + 24}$

$\sf{ \longrightarrow \: \dfrac{x}{2}+ 12 = \dfrac{x}{4}+ 24}$

$\sf{ \longrightarrow \: \dfrac{x}{2} - \dfrac{x}{4} = 24 - 12}$

$\sf{ \longrightarrow \: \dfrac{x}{4} = 12}$

$\sf{ \longrightarrow \: x = 12 \times 4}$

$\boxed{\sf{ \leadsto \: \sf{x = 48}}} \: \large{\red{ \star}}$

Therefore, the present age of his father is 48 years.

Now, the age of boy is, We got x as 48, Therefore,

$\sf{\longrightarrow \: \dfrac{48}{4}}$

$\boxed{\sf{\leadsto \: 12}} \: \large{\purple{ \star}}$

Therefore, the boy's age is 12 years.