Question

14. Trupti'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 Trupti's age to that of her grandfather?
​

Answer 1

Answer:

Let, Tanya's present age be x years

and Tanya's grandfather's age be yyears

Tanya's age 16 years ago =x−16 years

Tanya'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)

Tanya's age, 8 years from now =x+8

Tanya'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=128/5

Substituting x=128/5 in eq (i)

y=128×8/5 −112

=1024−560/5=464/5

Tanya's age, 8 years ago =128/5−8

=88/5

Tanya's grandfather's age, 8 years ago = 464/5−8=424/5

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

=11:53