Question

hey guys pls answer this question​

Answer 1

$\large{\underline{\red{\rm{AnswEr:}}}}$

$\bold\green{\underline{Given:}}$

10 years ago Amina's age was square of her sister's age

$\bold\orange{\underline{Let:}}$

The present age Amina be X

The present age her sister be y

10 years ago Amina and her sister's age

The age of Amina=X-10

The age of her sister=Y-10

Now,

⟹X-10=(y-10)²

⟹X-10=y²-20y+100--------(1)

Given,in the question again 11 years hence she will be 6 year's older than her sister's age

⟹X+11=(Y+11)+6

⟹X+11=Y+17

⟹X=Y+17-11

⟹X=Y+6---------(2)

Than

• putting the value of X=Y+6 in EQ 1

⟹X-10=Y²-20Y+100

⟹Y+6-10=Y²-20Y+100

⟹Y-4=Y²-20Y+10

⟹Y²-20Y-Y+100+4=0

⟹Y²-21Y+104=0

• Here splitting the middle term

⟹Y²-13Y-8Y+100=0

⟹Y(Y-13)-8(Y-13)=O

⟹(Y-8)(Y-13)=0

Thus, Y=8, 13

Here we have to choose the value of y according to the question

Now, putting the value of Y=13 in EQ 2

⟹X=Y+6

⟹X=13+6

⟹X=19

Hence,

$\bold\purple{\boxed{The\: present\: age\:of\:Amina=19\: years}}$

$\bold\orange{\boxed{The\: present\:age\:of\:her\: sister=13\: years}}$