Question

The present ages of a Father and Son is 13:11. 9 years ago the ratio of their ages was 5:4. Find the difference in the Father’s present age and the Son’s age 5 years later?

Answer 1

Answer :-

The difference in the Father’s present age and the Son’s age 5 years later = 1 year.

Solution :-

Case - I :

Condition - The present ages of a Father and Son is 13 : 11

Let the father's present age be 13x and son's present age be 11x.

Case - II :

Condition - 9 years ago the ratio of their ages was 5 : 4

Father's age 9 years ago = 13x - 9

Son's age 9 years ago = 11x - 9

Equation -

$\tt{ = > \dfrac{13x - 9}{11x - 9} = \dfrac{5}{4} } \\ \\ \tt{cross \: \: multiplying} \\ \\ \tt{ = > (13x - 9)4 =(11x - 9)5} \\ \\ \tt{ = > 52x - 36 = 55x - 45} \\ \\ \tt{ = > 45 - 36 = 55x - 52x} \\ \\ \tt{ = > 9 = 3x} \\ \\ \tt{ = > \dfrac{9}{3} = x} \\ \\ \tt{ = > x = 3}$

Value of x = 3

Father's present age = 13 × 3 = 39

Son's present age = 11 × 3 = 33

Son's age after 5 years = 33 + 5 = 38 years

The difference in the Father’s present age and the Son’s age 5 years later

= 39 - 38

= 1 years.

More Questions to solve :-

1. Ten years ago, a father was 12 times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.

Answer - brainly.in/question/40254456

2. The present age of Arjun's mother is three times the present age of Arjun. After 5 years their ages will add to 66 years. Find their present age?

Answer :- brainly.in/question/40419794