Question

Shane's age is 1/6 of his grandfather's age. Shane's mother is 2/3 the age of Shane's grandfather. What fraction is Shane's age to his mother's age?

Answer 1

Given :

Shane's age is 1/6 of grandfather's age.

Mother's age is 2/3 of grandfather's age.

To find :

The fraction of Shane's age to mother's age.

Solution :

Let Shane's age of x years.

Let Grandfather's age of y years.

According to the question,

Age of Rohit in terms of Grandfather,

$\sf \dashrightarrow y \times \dfrac{1}{6} = x$

$\sf \dashrightarrow \dfrac{1y}{6} = x$

$\sf \dashrightarrow \dfrac{y}{6} = x \: \: --- (i)$

Let mother's age be z.

Age of mother in terms of Grandfather.

$\sf \dashrightarrow y \times \dfrac{2}{3} = z$

$\sf \dashrightarrow \dfrac{2y}{3} = z \: \: --- (ii)$

We should find the fraction of Shane's age to mother's age. So,

$\sf \dashrightarrow \dfrac{Shane's \: age}{Mother's age} = \dfrac{x}{z}$

Substitute the values of x and z.

$\sf \dashrightarrow \dfrac{x}{z} = \dfrac{\dfrac{y}{6}}{\dfrac{2y}{3}}$

$\sf \dashrightarrow \dfrac{x}{z} = \dfrac{y}{6} \times \dfrac{3}{2y}$

$\sf \dashrightarrow \dfrac{x}{z} = \dfrac{3y}{12y}$

$\sf \dashrightarrow \dfrac{x}{z} = \dfrac{y}{4y}$

$\sf \dashrightarrow \dfrac{x}{z} = \dfrac{1}{4}$

Hence, the fraction of Shane's age to mother's age is 1/4.