Question

mother is 25 year older than her son. Son's age if after 8 year ratio of the son is to mother age will be 4/9

Answer 1

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Present age of Son = 12 years

$\bold{\underline{\underline{\large{\mathcal{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Mother is 25 year older than her son
• After 8 year ratio of the son's age to mother age will be $\bold{\dfrac{4}{9}}$

To FiNd :

• Present age of Son

SoLuTiOn :

Let the present age of Son be x years.

$\sf{\underline{\underline{As\:PeR\:tHe\:FiRsT\:cOnDiTiOn:}}}$

• Mother is 25 year older than her son

•°• Present age of Mother,

• $\sf{x\:+\:25\:years}$

$\sf{\underline{\underline{As\:PeR\:tHe\:SeCoNd\:cOnDiTiOn:}}}$

• After 8 year ratio of the son's age to mother age will be $\bold{\dfrac{4}{9}}$

Age after 8 years :

Son's age = x + 8 years

Mother's age = x + 25 + 8

•°• Mother's age = x + 33 years

Constituting it mathematically,

$\longrightarrow$ $\sf{\dfrac{x\:+\:8}{x\:+\:33}}$ = $\sf{\dfrac{4}{9}}$

Cross multiplying,

$\longrightarrow$ $\sf{9(x+8)\:=\:4\:(x\:+\:33)}$

$\longrightarrow$ $\sf{9x\:+\:72\:=\:4x\:+\:132}$

$\longrightarrow$ $\sf{9x\:-\:4x\:=\:132\:-\:72}$

$\longrightarrow$ $\sf{5x\:=\:132\:-\:72}$

$\longrightarrow$ $\sf{5x\:=\:60}$

$\longrightarrow$ $\sf{\:x\:=\:{\dfrac{60}{5}}}$

$\longrightarrow$ $\sf{x\:=\:12}$

•°• Present age of Son = x = 12 years

Present age of Mother = x + 25

Present age of Mother = 12 + 25

•°• Present age of Mother = 37 years

Answer 2

Answer:

\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}

AnsWer:

Present age of Son = 12 years

\bold{\underline{\underline{\large{\mathcal{StEp\:by\:stEp\:explanation:}}}}}

StEpbystEpexplanation:

GiVeN :

Mother is 25 year older than her son

After 8 year ratio of the son's age to mother age will be \bold{\dfrac{4}{9}}

9

4

To FiNd :

Present age of Son

SoLuTiOn :

Let the present age of Son be x years.

\sf{\underline{\underline{As\:PeR\:tHe\:FiRsT\:cOnDiTiOn:}}}

AsPeRtHeFiRsTcOnDiTiOn:

Mother is 25 year older than her son

•°• Present age of Mother,

\sf{x\:+\:25\:years}x+25years

\sf{\underline{\underline{As\:PeR\:tHe\:SeCoNd\:cOnDiTiOn:}}}

AsPeRtHeSeCoNdcOnDiTiOn:

After 8 year ratio of the son's age to mother age will be \bold{\dfrac{4}{9}}

9

4

Age after 8 years :

Son's age = x + 8 years

Mother's age = x + 25 + 8

•°• Mother's age = x + 33 years

Constituting it mathematically,

\longrightarrow⟶ \sf{\dfrac{x\:+\:8}{x\:+\:33}}

x+33

x+8

= \sf{\dfrac{4}{9}}

9

4

Cross multiplying,

\longrightarrow⟶ \sf{9(x+8)\:=\:4\:(x\:+\:33)}9(x+8)=4(x+33)

\longrightarrow⟶ \sf{9x\:+\:72\:=\:4x\:+\:132}9x+72=4x+132

\longrightarrow⟶ \sf{9x\:-\:4x\:=\:132\:-\:72}9x−4x=132−72

\longrightarrow⟶ \sf{5x\:=\:132\:-\:72}5x=132−72

\longrightarrow⟶ \sf{5x\:=\:60}5x=60

\longrightarrow⟶ \sf{\:x\:=\:{\dfrac{60}{5}}}x=

5

60

\longrightarrow⟶ \sf{x\:=\:12}x=12

•°• Present age of Son = x = 12 years

Present age of Mother = x + 25

Present age of Mother = 12 + 25

•°• Present age of Mother = 37 years