Question
Quantity I: ‘X’ – For a
number greater than one, the difference between the number and its reciprocal is equal to 40% of the sum of the number and its reciprocal. The square of this number is approximately 'X' % less than its cube (rounded to the nearest integer). Quantity II: ‘Y’ – Arjun’s income is 20% higher than Bhanu’s, while Chintu’s income is 68% lower than the combined incomes of Arjun and Bhanu. The income of Chintu is 'Y' % less than Arjun’s income. In the question, two Quantity I and Quantity II are given. You have to solve both the Quantities to establish the correct relation between Quantity I and Quantity II.Solution
ATQ,
Let the number is = 'n' (n + 1/n) × 0.4 = n – 1/n 0.4n + 0.4/n = n – 1/n 0.6n = 1.4/n n2 = 1.4/0.6 = 7/3 n3 = (7/3)√(7/3) X = [(7/3)√(7/3) – 7/3]/(7/3) × 100 = [√(7/3) – 1] × 100 = 52.75% - Quantity I Income of Bhanu = 100 Rs. , Income of Arjun = 1.2 × 100 = 120 Rs. Income of Chintu = (100 + 120) × 0.32 = 220 × 0.32 = 70.4 Y = (120 – 70.4)/120 × 100 = 41.33% - Quantity II Hence, Quantity I > Quantity II
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