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Sudha's grandfather was 8 time 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 Sudha's age to that of her grandfather?
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- 11 : 50
- 3 : 8
- 1 : 5
- 1 : 2
Correct Option: A
Let us assume 16 years ago, the age of Sudha and her grandfather were x and 8x years respectively; then
Present age of Sudha = x + 16
Present age of her grandfather = 8x + 16
After 8 years age of sudha from now = x + 16 + 8
After 8 years age of grandfather from now = 8x + 16 + 8
now according to question,
He would be 3 times of her age 8 years from now.
3(x + 16 + 8) = 8x + 16 + 8
⇒ 3x + 72 = 8x + 24
⇒ 5x = 48
∴ x = 48/5
Eight years ago , sudha age = x + 16 - 8 = x + 8
Eight years ago , grandfather age = 8x + 16 - 8 = 8x + 8
Hence, required ratio = (x + 8) / (8x + 8 )
Put the vale of x , we will get
⇒ required ratio = (48/5 + 8) / ( 8 x 45/5 + 8)
⇒ required ratio = ((48 + 40)/5) / ( (8 x 45 + 40)/5)
⇒ required ratio = (88/5) / ( 400/5)
⇒ required ratio = 88 / 400
⇒ required ratio = 11 : 50
