Question

5. Soma’s mother is 12 years more than twice soma’s age. After 8years, she will
be 20 years less than three times Soma’s age. Find Soma’s age and Soma’s
mother’s age? (3 Marks)

Answer 1

Given :

• Soma’s mother is 12 years more than twice soma’s age.
• After 8 years, she will
• be 20 years less than three times Soma’s age.

To Find :

• Present age of Soma.
• Present age of Soma's mother.

Solution :

Let the present age of Soma's mother be x years.

Let the present age of Soma be y years.

Case 1 :

Soma's mother is 12 years more than twice Soma's age.

Equation :

$\sf{\longrightarrow{x=2y+12\:\:\:\:(1)}}$

Case 2 :

After 8 years, mother will be 20 years, less than three times Soma's age.

Soma's mother age after 8 years, (x+8) years.

Soma's age after 8 years, (y+8) years.

Equation :

$\sf{\longrightarrow{(x+8)=3(y+8)-20}}$

$\sf{\longrightarrow{x+8=3y+24-20}}$

$\sf{\longrightarrow{x+8=3y+4}}$

$\sf{\longrightarrow{2y+12+8=3y+4}}$

$\bold{\Big[From\:equation\:(1)\:x\:=\:2y+12\Big]}$

$\sf{\longrightarrow{2y+20=3y+4}}$

$\sf{\longrightarrow{2y-3y=4-20}}$

$\sf{\longrightarrow{-y=-16}}$

$\sf{\longrightarrow{y=16}}$

Substitute, y = 16 in equation (1),

$\sf{\longrightarrow{x=2y+12}}$

$\sf{\longrightarrow{x=2(16)+12}}$

$\sf{\longrightarrow{x=32+12}}$

$\sf{\longrightarrow{x=44}}$

$\large{\boxed{\bold{Present\:age\:of\:mother\:=x\:=\:44\:years}}}$

$\large{\boxed{\bold{Present\:age\:of\:Soma\:=y\:=\:16\:years}}}$