math question answer please
Answers
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}↦Granddaughter
′
spresentage=yyears
\mapsto \bf{Grandfather's\: present\: age =\: 10y\: years}↦Grandfather
′
spresentage=10yyears
According to the question,
\implies \sf 10y =\: y + 54⟹10y=y+54
\implies \sf 10y - y =\: 54⟹10y−y=54
\implies \sf 9y =\: 54⟹9y=54
\implies \sf y =\: \dfrac{\cancel{54}}{\cancel{9}}⟹y=
9
54
\implies \sf y =\: \dfrac{6}{1}⟹y=
1
6
\implies \sf\bold{\purple{y =\: 6\: years}}⟹y=6years
Hence, the required ages of granddaughter and grandfather are :
➲ Present age of Granddaughter :
\longrightarrow \sf Present\: Age_{(Granddaughter)} =\: y\: years⟶PresentAge
(Granddaughter)
=yyears
\longrightarrow \sf\bold{\red{Present\: Age_{(Granddaughter)} =\: 6\: years}}⟶PresentAge
(Granddaughter)
=6years
➲ Present age of Grandfather :
\longrightarrow \sf Present\: Age_{(Grandfather)} =\: 10y\: years⟶PresentAge
(Grandfather)
=10yyears
\longrightarrow \sf Present\: Age_{(Grandfather)} =\: 10 \times 6\: years⟶PresentAge
(Grandfather)
=10×6years
\longrightarrow \sf\bold{\red{Present\: Age_{(Grandfather)} =\: 60\: years}}⟶PresentAge
(Grandfather)
=60years
{\small{\bold{\underline{\therefore\: The\: present\: age\: of\: granddaughter\: and\: grandfather\: is\: 6\: years\: and\: 60\: years\: respectively\: .}}}}
∴Thepresentageofgranddaughterandgrandfatheris6yearsand60yearsrespectively.