Question

Kiya's grandfather was 8 times older to her
16 years ago. He would be 3 times of her
age 8 years from now. Eight years ago, what
was the ratio of Kiya's age to that of her
grandfather?​

Answer 1

Answer:

Step-by-step explanation:let, Kiya's present age be x years

and Kiya's grandfather's age be yyears

Kiya's age 16 years ago =x−16 years

Kiya's  grandfather's age =y−16 years

A.T.Q,

y−16=8(x−16)

⟹y−16=8x−128

y=8x−128+16

y=8x−112    --------(i)

Kiya's age, 8 years from now =x+8

Kiya's grandfather's age, 8 years from now =y+8

A.T.Q,

y+8=3(x+8)

⟹8x−112+8=3(x+8)  -----from (i)

⟹8x−104=3x+24

⟹8x−3x=24+104

⟹5x=128

⟹x=5128​

Substituting x=5128​ in eq (i)

y=5128×8​−112

=51024−560​=5464​

Kiya's age, 8 years ago =5128​−8

=588​

Kiya's grandfather's age, 8 years ago =5464​−8=5424​

Ratio of Kiya's age to Kiya's grandfather's age =88:424

=11:53