Question

Ajay’s mother is four times as old as Ajay . After five years ,

his mother will be three times as old as he will be then .

What are their present ages ?

Answer 1

Step-by-step explanation:

Let the present age of Ajay = x.

Then the present age of Ajay's Mother = 4x

After five years,

Age of Ajay = x + 5

Age of his mother = 4x + 5

A/Q,

3(x + 5) = 4x + 5

➻ 3x + 15 = 4x + 5

➻ 3x + 15 - 4x = 5

➻ -x + 15 = 5

➻ -x = 5 - 15

➻ -x = -10

➻ x = 10.

Therefore,

Present age of Ajay = x = 10years.

Present age of Ajay's Mother = 4x

= 4×10 = 40years.

Verification

Putting x = 10 on the LHS

3(10 + 5)

= 30 + 15

= 45.

Putting x = 10 on the RHS

4×10 + 5

= 40 + 5

= 45

45 = 45

LHS = RHS

Hence, verified! ✓.

Steps for solving linear equations based word problems

• Read the problem carefully to analyse the facts given.

• Denote the unknown quantity by x or by any other variable.

• Express all other quantities mentioned in the problem in terms of the variable.

• Frame an equation by using the conditions of the problems.

• Solve the equation to find the value of the variable or the unknown. If the conditions of the given problem are satisfied by the value of the unknown, the solution is correct.

Answer 2

Given :

• Ajay's mother is four times as old as Ajay. After 5 years his mother will be three times as old as he will be than.

${\underline{\rule{200pt}{3pt}}}$

To Find :

• Find the present age.

${\underline{\rule{200pt}{3pt}}}$

Solution :

$\blue{❒}$According to Question :

✏ Let age of Ajay be y :

Ajay's mother is 4 times as old as Ajay .

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{Age \: of \: Mother}{Age \: of \: Ajay} = \dfrac{4 \times y}{y}}}}}}}{\bigstar}}$

After 5 years his mother will be three times as old as he will be than.

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{4y + 5}{y + 5} = \dfrac{3}{} }}}}}}{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\blue{❒}$Let's Cross Multiply :

${\longmapsto{\qquad{\sf{ 3(y + 5) = 4y + 5 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 3y + 15 = 4y + 5 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 4y - 3y = 15 - 5 }}}} \\ \\ \ {\qquad{\sf{Value \: of \: y \: = {\pink{\sf{10}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\blue{❒}$Calculating the Ages :

$\large{\orange{\dashrightarrow{\underline{\underline{\purple{\sf{ Ajay = y = 10 \: years }}}}}}}$

$\large{\orange{\dashrightarrow{\underline{\underline{\purple{\sf{ Ajay's \: Mother = 4y = 4 \times 10 = 40 \: years }}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\blue{❒}$Therefore :

❝ Present age of son is 10 years and age of mother is 40 years. ❞

$\\ \\ {\underline{\rule{200pt}{8pt}}}$