26) A boy's age is one-fourth that of his father. After24 years the bo

1.	26) A boy's age is one-fourth that of his father. After24 years the boy will be half the age of his father.Find their present ages.
Answer» 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.