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?

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For such problems, trial and error can help when dealing with square and cube numbers, especially in age-related questions.
Updated On: Mar 7, 2025
  • 39 years
  • 10 years
  • 38 years
  • 64 years
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The Correct Option is C

Solution and Explanation

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.
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