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For a number greater than one, the difference between itself and its reciprocal is 2% of the sum of itself and its reciprocal. By how much percentage (nearest to an integer) is the square of the number less than its cube?

For a number greater than one, the difference between itself and its reciprocal is 2% of the sum of itself and its reciprocal. By how much percentage (nearest to an integer) is the square of the number less than its cube? Correct Answer 1.88

Calculation:

Let the number be x.

⇒ (2/100) of

⇒ 0.02 ×

According to question,

x – (1/x) = 0.02 ×

⇒ 0.98x = 1.02/x

⇒ x2 = 1.04

⇒ x3 = 1.06

Required percentage =  × 100

⇒  × 100

⇒ (0.02/1.06) × 100

⇒ 1.88%

∴ The required percentage is 1.88%

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