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 following ratios.
(1) Ratio of Shubham’s age today to his mother’s age today.
(2) Ratio of Shubham’s mother’s age today to his father’s age today
(3) 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

(1)
Ratio of Shubham’s age today to his mother’s age today = Shubham’s age today : Shubham’s mother age today

= 12 years : 36 years

= $\frac{12}{36}$

= $\frac{12÷12}{36÷12}$ (HCF of 12 and 36 = 12)

= $\frac{1}{3}$

= 1 : 3

Thus, the ratio of Shubham’s age today to his mother’s age today is $\frac{1}{3}$ or 1 : 3.

(2)
Ratio of Shubham’s mother’s age today to his father’s age today = Shubham’s mother age today : Shubham’s father age today

= 36 years : 42 years

= $\frac{36}{42}$

= $\frac{36÷6}{42÷6}$ (HCF of 36 and 42 = 6)

= $\frac{6}{7}$

= 6 : 7

Thus, the ratio of Shubham’s mother’s age today to his father’s age today is $\frac{6}{7}$ or 6 : 7.

(3)
Difference between the present age of Shubham and when he was 10 year 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

= $\frac{10}{34}$

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

= $\frac{5}{17}$

= 5 : 17

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