Question

A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.​

Answer 1

Answer:

Given :-

• A grandfather is ten times older than his granddaughter.
• He is also 54 years older than her.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf{Granddaughter's\: present\: age =\: y\: years}$

$\mapsto \bf{Grandfather's\: present\: age =\: 10y\: years}$

According to the question,

$\implies \sf 10y =\: y + 54$

$\implies \sf 10y - y =\: 54$

$\implies \sf 9y =\: 54$

$\implies \sf y =\: \dfrac{\cancel{54}}{\cancel{9}}$

$\implies \sf y =\: \dfrac{6}{1}$

$\implies \sf\bold{\purple{y =\: 6\: years}}$

Hence, the required ages of granddaughter and grandfather are :

➲ Present age of Granddaughter :

$\longrightarrow \sf Present\: Age_{(Granddaughter)} =\: y\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Granddaughter)} =\: 6\: years}}$

➲ Present age of Grandfather :

$\longrightarrow \sf Present\: Age_{(Grandfather)} =\: 10y\: years$

$\longrightarrow \sf Present\: Age_{(Grandfather)} =\: 10 \times 6\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Grandfather)} =\: 60\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: granddaughter\: and\: grandfather\: is\: 6\: years\: and\: 60\: years\: respectively\: .}}}}$