Tanya's grandfather was 8 times older to her 16 years ago. He would be

1.	Tanya'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 Tanya's age to that of her grandfather?1. 16 : 112. 11 : 533. 17 : 304. None of these
Answer» Correct Answer - Option 2 : 11 : 53 Calculation: Let, Tanya's present age be x years and Tanya's grandfather's age be y years Tanya's age 16 years ago = x − 16 years Tanya's grandfather's age = y − 16 years According to the question: y − 16 = 8(x − 16) ⇒ y − 16 = 8x − 128 ⇒ y = 8x − 128+ 16 ⇒ y = 8x − 112 ----(1) Tanya's age, 8 years from now = x + 8 Tanya's grandfather's age, 8 years from now = y + 8 Again,According to the question: y + 8 = 3(x + 8) ⇒ 8x − 112 + 8 = 3(x + 8) ⇒ 8x − 104 = 3x + 24 ⇒ 8x − 3x = 24 + 104 ⇒ 5x = 128 ⇒ x= 128/5 Putting the value of x = 128/5 in equation(1): y = 8x − 112 ⇒ y = 8× 128/5 - 112 ⇒ y = (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 ∴ The ratio of Tanya's age to that of her grandfather is 11 : 53.

Tanya'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 Tanya's age to that of her grandfather?1. 16 : 112. 11 : 533. 17 : 304. None of these

Answer» Correct Answer - Option 2 : 11 : 53

Calculation:

Let, Tanya's present age be x years

and Tanya's grandfather's age be y years

Tanya's age 16 years ago = x − 16 years

Tanya's grandfather's age = y − 16 years

According to the question:

y − 16 = 8(x − 16)

⇒ y − 16 = 8x − 128

⇒ y = 8x − 128+ 16

⇒ y = 8x − 112 ----(1)

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

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

Again,According to the question:

y + 8 = 3(x + 8)

⇒ 8x − 112 + 8 = 3(x + 8)

⇒ 8x − 104 = 3x + 24

⇒ 8x − 3x = 24 + 104

⇒ 5x = 128

⇒ x= 128/5

Putting the value of x = 128/5 in equation(1):

y = 8x − 112

⇒ y = 8× 128/5 - 112

⇒ y = (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

∴ The ratio of Tanya's age to that of her grandfather is 11 : 53.