Question

Three times Diana's age is $17$ years more than twice Jim's age. The sum of their ages is $13$ years less than their fathers age, which is three times Jims age. What are the children's ages?

• A. Diana $21$ years, Jim $16$ years
• B. Diana $15$ years, Jim $14$ years
• C. Diana $15$ years, Jim $16$ years
• D. Diana $20$ years, Jim $14$ years

Answer 1

The correct option is B Diana $15$ years, Jim $14$ years

Let Diana's age be $x$ and Jim's age be $y$
Their father's age $=3y$
Given, "Three times Diana's age is $17$ years more than twice Jim's age "

$=>3x=17+2y$

$=>3x-2y=17$ --- (1)
Also, " The sum of their ages is $13$ years less than their fathers age which is three times Jims age"
$=>x+y=3y-13$

$=>x-2y=-13$ --- (2)

Subtracting equation $\left(2\right)$ from $\left(1\right)$, we get

$2x=30$

$=>x=15$

Substituting $x=15$ in the equation $\left(2\right)$, we get

$15-2y=-13$

$=>2y=28$

$=>y=14$

Hence, their ages are Diana $=15$ years ; Jim's $=14$ years.