Question

the ratio between the present ages of child andhis teacher is 13:19 years hence the ratio of their age will be 1:2. What was the ratio of their ages 9 years ago. ​

Answer 1

Given : Ratio between the present ages of child and his teacher is 1 : 3

19 years hence the ratio of their age will be 1:2

To Find : ratio of their ages 9 years ago.

Solution:

Let say child age = A  years

Teacher age  = 3A  years

19 years after  child age = A + 9  years

19 years after Teacher age  = 3A+ 9  years

2(A + 19) =3A + 19

=> 2A + 38 = 3A  + 19

=> 19 = A

child age = 19  years

Teacher age  = 57  years

ages 9 years ago.  

Child = 19 - 9 = 10

Teacher = 57 - 9 = 48

Ratio  = 10 : 48

= 5 : 24

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