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

Hint:

Let John's age 5 years ago be x, set up two age equations for 5 years ago and 25 years from now, then solve for x.

Answer 1

The Correct Option is C

Step 1: Define present ages directly.
Let John's present age be $a$ and his grandfather's present age be $g$.

Step 2: Translate '5 years ago' into an equation.
Five years ago, John was $a-5$ and the grandfather was $g-5$. Since the grandfather was five times as old then, $g - 5 = 5(a-5)$, which gives $g = 5a - 20$.

Step 3: Translate '25 years from now' into an equation.
In 25 years, John will be $a+25$ and the grandfather will be $g+25$. Since the grandfather will be twice as old then, $g + 25 = 2(a+25)$, which gives $g = 2a + 25$.

Step 4: Solve the two equations together.
Setting the two expressions for $g$ equal: $5a - 20 = 2a + 25$, so $3a = 45$, giving $a = 15$. Then $g = 2(15) + 25 = 55$.

Step 5: Form the ratio.
John's age to grandfather's age $= 15:55 = 3:11$, the same result as before.

Final Answer:
The ratio is 3:11. \[ \boxed{3:11} \]