Question

Shahil’s mother is seven times older than him. Four years from now,she will be your

times as old as Shahil will then be. What are their present ages?​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that Shahil’s mother is seven times older than him and four years from now,she will be four times as old as Shahil will then be. We have to find their present ages.

We'll first assume their present ages as two variables, say x and y. After that, we'll form algebraic equations according to the given information in the question. By solving the equations, we'll find the value of x and y i.e, their present ages.

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

Let,

● Present age of Shahil = x years.

● Present age of Shahil's mother = y years.

According to the question ,

$\longmapsto$ Shahil's mother's age = 7 × Shahil's age

$\longmapsto$ y = 7x

Let it be the equation (1).

Also,

» Four years from now,she will be your times as old as Shahil will then be.

Their ages after 4 years :

• Shahil's mother's age = y + 4
• Shahil's age = x + 4

Equation formed according to the question :

After 4 years :

$\longrightarrow$ Shahil's mother's age [After 4 years] = 4 ( Shahil's age [After 4 years] )

$\longrightarrow \sf {y + 4 = 4 ( x + 4 )}$

Substitute the value of y from the equation 1.

$\longrightarrow \sf {7x + 4 = 4 ( x + 4 )}$

$\longrightarrow \sf {7x + 4 = 4 ( x ) + 4(4 )}$

$\longrightarrow \sf {7x + 4 = 4x + 16}$

$\longrightarrow \sf {7x - 4x = 16 - 4}$

$\longrightarrow \sf {3x= 12}$

$\longrightarrow \sf {x= \cancel { \dfrac{12}{3} } }$

$\longrightarrow \sf {x= 4}$

$\longrightarrow \sf \red {Shahil's \: age= 4 \: years }$

Also, from the equation ( 1 ) :

$\longrightarrow \sf {y= 7x}$

$\longrightarrow \sf {y= 7(4)}$

$\longrightarrow \sf {y= 28}$

$\longrightarrow \sf \red {Mother's \: age = 28 \: years }$

Therefore,

• ❝ Present age of Shahil is 4 years .❞
• ❝ Present age of Shahil's mother is 28 years.❞