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 father's age which is three times Jim's 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

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 (2) from (1), we get 

2x = 30

⇒ x = 15

Substituting x = 15 in the equation (2), we get 

15 − 2y = −13

⇒ 2y = 28

⇒ y = 14

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