Question

${ \large︎{ \underline{ \sf{ \pmb{ \red{Question}}}}}}$

At present, the age of asha's mother is 4 times the age of asha. Three years ago the age of asha's mother was five times the age of asha. Find their present ages. ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, at present, the age of asha's mother is 4 times the age of asha.

Let assume that

Present age of Asha be x years.

So, Present age of Asha's mother = 4x years.

According to statement, Three years ago the age of asha's mother was five times the age of asha.

So, three years ago

Age of Asha = (x - 3) years

Age of Asha's mother = (4x - 3) years

Now, it is given that, the age of asha's mother was five times the age of asha.

$\rm \: 4x - 3 = 5(x - 3)$

$\rm \: 4x - 3 = 5x -15$

$\rm \: 4x - 5x = 3 -15$

$\rm \: - x = -12$

$\rm\implies \:x = 12$

Hence,

Present age of Asha = 12 years.

Present age of Asha's mother = 4 × 12 = 48 years.

Verification :-

Present age of Asha = 12 years.

Present age of Asha's mother = 4 × 12 = 48 years.

It means, Asha's mother is 4 times of Asha age.

Now, 3 years ago

Age of Asha = 9 years

Age of Asha's mother = 45 years

It means, Asha's mother is 5 times of Asha age.

Hence, Verified

Answer 2

Answer:

Given :-

• At present, the age of Asha's mother is 4 times the age of Asha.
• Three years ago the age of Asha's mother was five times the age of Asha.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Asha)} =\: x\: years$

$\mapsto \bf Present\: Age_{(Asha's\: Mother)} =\: 4x\: years$

❒ Three years ago :

$\leadsto \sf Age_{(Asha)} =\: (x - 3)\: years$

$\leadsto \sf Age_{(Asha's\: Mother)} =\: (4x - 3)\: years$

According to the question :

$\bigstar$ Three years ago, the age of Asha's mother was five times the age of Asha.

So,

$\implies \bf 4x - 3 =\: 5(x - 3)$

$\implies \sf 4x - 3 =\: 5x - 15$

$\implies \sf 4x - 5x =\: - 15 + 3$

$\implies \sf {\cancel{-}} x =\: {\cancel{-}} 12$

$\implies \sf\bold{\purple{x =\: 12}}$

Hence, the required present ages are :

$\dag$ Present Age Of Asha :

$\dashrightarrow \sf Present\: Age_{(Asha)} =\: x\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Asha)} =\: 12\: years}}$

$\dag$ Present Age Of Asha's Mother :

$\dashrightarrow \sf Present\: Age_{(Asha's\: Mother)} =\: 4x\: years$

$\dashrightarrow \sf Present\: Age_{(Asha's\: Mother)} =\: (4 \times 12)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Asha's\: Mother)} =\: 48\: years}}$

$\therefore$ The present age of Asha is 12 years and the present age of Asha's mother is 48 years .