Question

Ram's age was square of a number last year and it will be cube of a number next year. How long must he wait before his age is again the cube of a number?

• A. 39 years
• B. 10 years
• C. 38 years
• D. 64 years

Hint:

For such problems, trial and error can help when dealing with square and cube numbers, especially in age-related questions.

Answer 1

The Correct Option is C

Step 1: Let Ram's age last year be \( x^2 \) and next year be \( y^3 \), where \( x \) and \( y \) are natural numbers.
Step 2: The age difference between last year and next year is: \[ y^3 - x^2 = 2 \]
Step 3: Solve for \( x \) and \( y \). After trial and error, we get that \( x = 6 \) and \( y = 7 \).
Step 4: Therefore, Ram's age last year is \( 6^2 = 36 \), and next year it will be \( 7^3 = 343 \).
Step 5: The age difference between now and next year is \( 343 - 36 = 307 \). Ram needs to wait \( 307 \) years.