Question

Rashmi mother isfour time as old as Rashmi after 5year her mother will be three times as old as she will be then find their presents ages​

Answer 1

Answer:

Present age of Rashmi = 10 years

Present age of Rashmi's mother = 40 years

$\rule{100}2$

Step-by-step-explanation:

$\sf{\red{Method\:1)}}$

Let the present age of Rashmi be x years and present age of Rashmi's mother be y years.

$\sf{\underline{\underline{After\:5\:years}}}$

• Age of Rashmi = (x + 5) years
• Age of Rashmi's mother = (y + 5) years

$\sf{\underline{\underline{According\:to\:quetion,}}}$

Rashmi mother is four time as old as Rashmi. After 5 years her mother will be three times as old as she.

Here are two cases in this question.

Case 1)

Rashmi mother is four time as old as Rashmi.

=> $\sf{y\:=\:4(x)}$

=> $\sf{y\:=\:4x}$ ...(1)

Case 2)

After 5 years her mother will be three times as old as she.

=> $\sf{y\:+\:5\:=\:3(x\:+\:5)}$

=> $\sf{4x\:+\:5\:=\:3x\:+\:15}$ [From (1)]

=> $\sf{4x\:-\:3x\:=\:15\:-\:5}$

=> $\sf{x\:=\:10}$

Substitute value of x = 10 in equation (1)

=> $\sf{y\:=\:4(10)}$

=> $\sf{y\:=\:40}$

•°• Age of Rashmi is 10 years and age of Rashmi's mother is 40 years.

$\rule{200}2$

$\sf{\red{Method\:2)}}$

Rashmi mother is four time as old as Rashmi.

$\sf{\underline{\underline{Assume }}}$

Let present age of Rashmi be x years.

$\therefore$ Present age of Rashmi's mother = 4x years.

After 5 years her mother will be three times as old as she.

$\sf{\underline{\underline{According\:to\:quetion,}}}$

=> $\sf{4x\:+\:5\:=\:3(x\:+\:5)}$

=> $\sf{4x\:+\:5\:=\:3x\:+\:15}$

=> $\sf{4x\:-\:3x\:=\:15\:-\:5}$

=> $\sf{x\:=\:10}$

$\therefore$ Present age of mother = $\sf{4(10)}$

=> $\sf{40}$

•°• Age of Rashmi is 10 years and age of Rashmi's mother is 40 years.

Answer 2

Answer :-

Given :-

• Rashmi's mother is 4 times old as that of the age of Rashmi

• After 5 years the age of her mother will be three times as old as she will be

To find :-

• Rashmi and her mother's present age = ?

Solution :-

Let the age of Rashmi will be :- x

Then , the age of Rashmi's mother will be :- 4x

After 5 years the age of Rashmi will be :- x + 5

After 5 years the age of Rashmi's mother will be :- 4x + 5

According to the question ,

3 ( x + 5 ) = 4x + 5

=> 3x + 15 = 4x + 5

=> 15 - 5 = 4x - 3x

=> x = 10

Therefore , the present age of Rashmi is 10 years old and the present age of Rashmi's mother is 40 years .