Question

simran mother is thrice as old as simran after 10 years.simran will become half the age of mother.find their present ages.​

Answer 1

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

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

• Simran's mother is thrice as old as Simran
• After 10 years Simran will become half the age of Mother

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

• Present age of Simran
• Present age of Mother.

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

Let the present age of Mother be x years.

Let the present age of Simran be y years.

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

• Simran's mother is thrice as old as Simran

Representing the condition mathematically,

x = 3y ---> 1

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

• After 10 years.simran will become half the age of Mother

Ages after 10 years :-

Mother = x + 10 years

Simran = y + 10 years

Representing the second condition mathematically.

=> y + 10 = $\frac{1}{2}$ ( x + 10)

=> y + 10 = $\frac{x + 10}{2}$

Cross multiplying,

=> 2 ( y + 10) = x + 10

=> 2y + 20 = x + 10

=> x + 10 = 2y + 20

=> x - 2y = 20 - 10

=> x - 2y = 10 ----> 2

Substitute x = 3y from equation 1 in equation 2 for x,

=> 3y - 2y = 10

=> y = 10

Substitute value of y in equation 2,

=> x - 2y = 10

=> x - 2 ( 10) = 10

=> x - 20 = 10

=> x = 10 + 20

=> x = 30

•°• Present age of Mother = x = 30 years

Present age of Simran = y = 10 years.

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

For first condition :-

Present age of Mother = x = 30

Present age of Simran = y = 10

=> x = 3y

Plug in the values,

=> 30 = 3 (10)

=> 30 = 30

LHS = RHS.

For second condition :-

Ages after 10 years :-

Mother's age = x + 10 years = 30 + 10 = 40 years

Simran's age = y + 10 years = 10 + 10 = 20 years.

=> y + 10 = $\frac{1}{2}$ ( x + 10)

Plug in the values,

=> 20 = $\frac{1}{2}$ × 40

=> 20 = $\frac{40}{2}$

=> 20 = 20

LHS = RHS.

Hence verified.