Question

Ramola's grandmother's present ages 6 times as Ramola's present age. Three years before Ramola's grandmother's age was 8 times Ramola's age. find their present ages. with solution​

Answer 1

Given:

• Ramola's grandmother present age is 6 times as ramola's present age

• three years before,ramola's grandmother age was 8 times ramolas age

To Find:

present age of ramola and ramola's grandmother

Solution:

let their present age of ramola be "x"

and ramola's grandmother age be "y"

three years before,ramola and her grandmother age will be 3 less than their present age

thus,

we get the age of ramola and her grandmother 3 years before as:

•$\sf{ x\: - \:3}$

•$\sf{ y\: -\: 3}$

now,it is given that,

the present age of ramola's grandmother is 6 times ramolas present age

thus,we get the equation:

➛ $\sf{y\: =\: 6x}$ ........(1)

it is given that,

the age of ramola's grandmother 3 years before, was 8 times ramola's age at that time

So , we get the equation:

➛$\sf{ y\: -\: 3\: = \:8( x - 3)}$ ........(2)

now, we will solve the two equation to get the value of "x" and "y"

Substituting y = 6x in the equation,

$\sf{ y\: -\: 3\: =\: 8(x - 3)}$

we get,

$➙$ $\sf{6x\: - \:3\: = \:8(x -3)}$

$➙$ $\sf{6x \:-\: 3 \:=\: 8x\: - \:24}$

Subtracting 6x from both sides,we get:

$⟹$ $\sf{6x - 3 - 6x = 8x - 24 - 6x}$

$⟹$$\sf{ -3 = 2x - 24}$

adding 24 to both side of the equation,we get:

$⟹$$\sf{ -3 + 24 = 2x - 24 + 24}$

$⟹$ $\sf{21 = 2x}$

Dividing both sides by 2, we get the value of x:

$⟹$$\tt{x = \frac{21}{2} \: = 10.5}$

Therefore,

present age of ramola is 10.5 years

Now,

substituting 10.5 for x in the expression "y = 6x"

we get,

present age of ramola's grandmother

$⟹$$\sf{ 6x = 6 × 10.5 = 63\:years}$

Hence,

$⊱ \rm\underline{\:present\: age \:of\: ramola\: is\: 10.5 \:years}$

$⊱ \rm\underline{ \:present\: age\: of\: ramola's\: grandmother\: is\: 63\: years}$

Answer 2

Solution :

The present age of Ramola and her grandmother is 10.5 years and 63 years .

Step by step Explanatìon:

Let , The pesent age of Ramola be x

and Present age of Ramola's Grandmother be y

According to the Question :

Ramola's grandmother's present ages 6 times as Ramola's present age .

$\sf\implies\:y=6x.....(1)$

And , Three year before :

Ramola's Grandmother's age = y -3

and Ramola's age = x-3

According to the Question :

Three years before Ramola's grandmother's age was 8 times Ramola's age.

$\sf\implies\:y-3=8(x-3)...(2)$

Now , put the value of y= 6x in equation (2) , Then

$\sf\implies\:6x-3=8(x-3)$

$\sf\implies\:6x-3=8x-24$

$\sf\implies\:8x-6x=24-3$

$\sf\implies\:2x=21$

$\sf\implies\:x=\dfrac{21}{2}$

$\sf\implies\:x=10.5$

Hence,

• Ramola's present age , x = 10.5 years
• and Ramola's Grandmother age ,y = 6x = 63 years