Question

Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.

Answer 1

Shubham’s age today = 12 years

Shubham’s father age today = 42 years

∴ Shubham’s mother age today = Shubham’s father age today − 6 years

= 42 years − 6 years

= 36 years

Difference between the present age of Shubham and when he was 10 years old

= 12 years − 10 years = 2 years

∴ Shubham's mother age when Shubham was 10 years old

= 36 years − 2 years = 34 years

Ratio of Shubham’s age to his mother’s age when Shubham was 10 years old 

= 10 years : 34 years

= ${\displaystyle \frac{10}{34}}$

= ${\displaystyle \frac{10÷2}{34÷2}}$     (HCF of 10 and 34 = 2)

= ${\displaystyle \frac{5}{17}}$

= 5 : 17

Thus, the ratio of Shubham’s age to his mother’s age when Shubham was 10 years old is ${\displaystyle \frac{5}{17}}$ or 5 : 17.