Question

John's grandfather was five times older to him 5 years ago. He would be two times of his age after 25 years from now. What is the ratio of John's age to that of his grandfather ?

• A. 7:11
• B. 5:11
• C. 3:11
• D. 4:11

Answer 1

The Correct Option is C

To solve this problem, let's define variables for the current ages of John and his grandfather. Let John's current age be \( x \) years and his grandfather's age be \( y \) years.

We have two conditions:

1. Five years ago, John's grandfather was five times older than John.
   So, \( y - 5 = 5(x - 5) \).
2. After 25 years, John's grandfather will be twice the age of John.
   So, \( y + 25 = 2(x + 25) \).

Let's solve these two equations: 

From the first equation:

\( y - 5 = 5x - 25 \)
Rearrange it to find:

\( y = 5x - 20 \) --- (1)

From the second equation:

\( y + 25 = 2(x + 25) \)

\( y + 25 = 2x + 50 \)

Rearrange it to find:

\( y = 2x + 25 \) --- (2)

Let's equate (1) and (2):

\( 5x - 20 = 2x + 25 \)

Subtract \( 2x \) from both sides:

\( 3x - 20 = 25 \)

Add 20 to both sides:

\( 3x = 45 \)

Divide by 3:

\( x = 15 \)

So John's current age is 15 years.

Substitute \( x = 15 \) into equation (1):

\( y = 5(15) - 20 = 75 - 20 = 55 \)

So, the grandfather's current age is 55 years.

Therefore, the ratio of John's age to his grandfather's age is:

\(\frac{15}{55} = \frac{3}{11}\)

Hence, the ratio is 3:11.