Question

(v)
Sharda's mother's present age is 6 times Sharda's present age. Sharda's age five years
from now will be one third of her mother's present age. What are their present ages?​

Answer 1

Answer:Sharda is 5 years old and her mother is 30 years old...

:Plss give me brainly if my ans is clear to u...Thk u

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given:}}}}}$

• Sharda's mother's present age is 6 times Sharda's present age
• Sharda's age five years
• from now will be one third of her mother's present age

$\bf{\underline{\underline{\sf{\green{To\:find:}}}}}$

• Present age of Sharda's mother
• Present age of Sharda

$\bf{\underline{\underline{\sf{\green{Solution:}}}}}$

Let the present age of Sharda's Mother be x years.

Let the present age of Sharda be y years.

$\bf{\underline{\underline{\sf{\purple{As\:per\:the\:first \:condition:}}}}}$

• Sharda's mother's present age is 6 times Sharda's present age

Representing the condition mathematically to obtain our first equation.

=> Mother's age = 6 × Sharda's age

=> x = 6y ----> 1

$\bf{\underline{\underline{\sf{\purple{As\:per\:the\:second \:condition:}}}}}$

• Sharda's age five years
• from now will be one third of her mother's present age

Sharda's age 5 years after = y + 5

Sharda's Mother's age = x years

Representing second condition mathematically.

=> y + 5 = $\frac{1}{3}$ × x

=> y + 5 = $\frac{x}{3}$

Cross multiplying,

=> 3 ( y + 5) = x

=> 3y + 15 = x

=> x = 3y + 15

=> x - 3y = 15

=> x - 3y = 15 ---- > 2

Substitute value of x from equation 1 in equation 2 for x.

=> 6y - 3y = 15

=> 3y = 15

=> y = $\frac{15}{3}$

=> y = 5

Substitute y = 5 in equation 2,

=> x - 3y = 15

=> x - 3 ( 5) = 15

=> x - 15 = 15

=> x = 15 + 15

=> x = 30

$\bf{\large{\underline{\boxed{\sf{\blue{Present\:age\:of\:mother\:=\:\:x\:=\:\:30\:years}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\blue{Present\:age\:of\:Sharda\:\:\:y\:=\:5\:years}}}}}}$

$\bf{\huge{\underline{\boxed{\sf{\red{Verification:}}}}}}$

For first case :-

• Sharda's mother's present age is 6 times Sharda's present age

=> x = 6 ( y)

=> 30 = 6 ( 5)

=> 30 = 30

LHS = RHS.

For second case :-

• Sharda's age five years
• from now will be one third of her mother's present age

Sharda's age 5 years after = y + 5 = 5 + 5 = 10 years

Sharda's Mother's present age = 30 years = x

=> $\bf\frac{ y + 5}{x}$= $\bf\frac{1}{3}$

=> $\bf\frac{10}{30}$= $\bf\frac{1}{3}$

Dividing LHS by 10,

=> $\bf\frac{1}{3}$ = $\bf\frac{1}{3}$

LHS = RHS.

Hence verified