Question

A father is three times as old as his son. The sum of their ages is 52 years. Find the ages of son and father.​

Answer 1

Given : A father is three times as old as his son and sum of their ages is 52 years.

To Find : Ages of son and father.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀_______________

❍ Let the age of son be y. Then, father's will be 3y years as father is three times as old as his son.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀

Sum of their ages is 52 years.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀_______________

$\underline{\sf{★ \: According \: to \: the \: question : }}$

$\:$

$\sf : \implies \: 3y + y = 52 \\ \\ \\ \sf : \implies \:4y = 52 \\ \\ \\ \sf : \implies \:y = \cancel\frac{52}{4} \\ \\ \\ \sf : \implies \:\underline{\boxed{\sf\purple{y = 13}}} \: \bigstar$

$\:$

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀_______________

★ Now put the value found in their ages.

$\:$

• son's age = y = 13 years
• father's age = 3y = 39 years

$\:$

V E R I F I C A T I O N :

$\: \:$

$\sf : \implies \: 3y + y = 52 \\ \\ \\ \sf : \implies \:39 + 13= 52 \\ \\ \\\sf : \implies \:\underline{\boxed{\sf\purple{52 = 52}}} \: \bigstar$

$\:$

Hence, Verified !