Question

the present age of Ritesh is 1 by 5 times his mother Age. 5 year later his age will be 1 by 3 times his mother age of the time find their present age​

Answer 1

Let present age of Ritesh be "M" years and present age of mother be "N" years.

Present age of Ritesh is 1 by 5 times his mother age.

According to question,

=> $\sf{M\:=\:\frac{1}{5}N}$

=> $\sf{5M\:=\:N}$ ___ (eq 1)

5 year later his age will be 1 by 3 times his mother age.

Now,

• Age of Ritesh = (M + 5) years
• Age of mother = (N + 5) years

According to question,

=> $\sf{M\:+\:5\:=\:\frac{1}{3}(N\:+\:5)}$

=> $\sf{3(M\:+\:5)\:=\:N\:+\:5}$

=> $\sf{3M\:+\:15\:=\:N\:+\:5}$

=> $\sf{3M\:+\:15\:=\:5M\:+\:5}$ [From (eq 1)]

=> $\sf{5M\:-\:3M\:=\:15\:-\:5}$

=> $\sf{2M\:=\:10}$

=> $\sf{M\:=\:5}$

Substitute value of M in (eq 1)

=> $\sf{N\:=\:5(5)}$

=> $\sf{N\:=\:25}$

•°• Present age of Ritesh is 5 years.

Present age of his mother is 25 years.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Present age of Mother = 25 years

Present age of Ritesh = 5 years.

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• The present age of Ritesh is 1 by 5 times his mother age
• 5 years later his age will be 1 by 3 times his mother age

To find :

• Present age of Ritesh
• Present age of Mother

Solution :

Let the present age of Mother be x years.

$\bold{\underline{\underline{As\:per\:the\:question:}}}$

•°• Present age of Ritesh = $\bold{\dfrac{x}{5}}$

$\bold{\underline{\underline{As\:per\:the\:first\:condition:}}}$

• The present age of Ritesh is $\bold{\dfrac{1}{5}}$ times his mother age

Constituting it mathematically,

$\rightarrow$ $\bold{\dfrac{x}{5}}$ = $\bold{x}$ ---> (1)

$\bold{\underline{\underline{As\:per\:the\:second\:condition:}}}$

• 5 years later his age will be $\bold{\dfrac{1}{3}}$times his mother age

•°• Age 5 years later :

Mother = x + 5 years.

Ritesh = $\bold{\dfrac{x}{5}+5}$ years.

Constitute the second condition mathematically,

$\rightarrow$ $\bold{\dfrac{x}{5}+5}$ = $\bold{\dfrac{1}{3}}{\bold{\times\:x+5}}$

$\rightarrow$ $\bold{\dfrac{x+5(5)}{5}}$ = $\bold{\dfrac{x+5}{3}}$

$\rightarrow$ $\bold{\dfrac{x+25}{5}}$ = $\bold{\dfrac{x+5}{3}}$

Cross multiplying,

$\rightarrow$ $\bold{3(x+25)=5(x+5)}$

$\rightarrow$ $\bold{3x+75=5x+25}$

$\rightarrow$ $\bold{3x+75=5x+25}$

$\rightarrow$ $\bold{75-25=5x-3x}$

$\rightarrow$ $\bold{50=2x}$

$\rightarrow$ $\bold{2x=50}$

$\rightarrow$ $\bold{x={\dfrac{50}{2}}}$

$\rightarrow$ $\bold{x=25}$

•°• Present age of Mother = x = 25 years.

As mentioned in the question,

• The present age of Ritesh is 1 by 5 times his mother age

•°• Present age of Ritesh,

$\rightarrow$ $\bold{\dfrac{x}{5}}$

Substitute value of x,

$\rightarrow$ $\bold{\dfrac{25}{5}}$

$\rightarrow$ 5

•°• Present age of Ritesh = 5 years