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My grandfather was 8 times older than me 16 years ago. He will be 3 times my age 8 years from now. Eight years ago, what was the ratio of my age to that of my grandfather?

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1:2

1:5

13:18

11:53

answer is D.

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Detailed Solution

Concept- We will assume my age 16 years ago to be

x

, therefore according to the question, grandfather’s age was

8 x

then according to the given information we will form our equations as present age will be

x + 16

and

8 x + 16

. Also 8 years from now
age will be

x + 16 + 8

and

8 x + 16 + 8

that is

x + 24

and

8 x + 24

.
Then we have to find the ratio of my age to my grandfather's age. Let us assume that 16 years ago, my age was x, then the age of my grandfather will be

8 x

. From this assumption we get my present age =

x + 16

and also my grandfather’s present age =

8 x + 16

.
My age after 8 years will be

(x + 16 + 8) = (x + 24)

and age of my grandfather after 8 years will be

(8 x + 16 + 8) = (8 x + 24)

. Thus, we formulate the given situation as follows

3 (x + 24) = 8 x + 24

. Therefore, solving the equation further, we get

3 x + 72 = 8 x + 24

, grouping the similar terms together, we get

8 x - 3 x = 72 - 24

or 5 x = 48

5 x = 48

x = \frac{48}{5}

x = 9.6

Thus, 16 years ago my age was 9.6years and my grandfather’s age was

6 \times 8 = 76.8 years

. So, my present age will be

9.6 + 16 = 25.6 years

and my grandfather’s present age will be

76.8 + 16 = 92.8 years

.
Therefore, 8 years back the ratio of my age to that of my grandfather’s age will be

\frac{my present age - 8}{my grandfather^{'} s age - 8} = \frac{25.6 - 8}{92.8 - 8} = \frac{11}{53} = 11 : 53 .

Therefore, option 4 is correct.

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