With reference to a number greater than one, the difference between itself and its reciprocal is 25% of the sum of itself and its reciprocal. By how much percentage (correct one decimal place) is the fourth power of the number greater than its square?
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 66.7
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Understanding |
Application |
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Suppose the number is x. |
As given: x – 1/x = 0.25(x + 1/x) ⇒ x2 – 1 = 0.25(x2 + 1) ⇒ 0.75x2 = 1.25 ⇒ x2 = 5/3 And x4 = 25/9 Hence, Required percentage = [(25/9 – 5/3)/5/3] × 100 = [(10/9)/(5/3)] × 100 = 200/3 = 66.7% |