Quantity 1: Q : A number, greater than one, the difference between itself and its reciprocal is 40% of the sum of itself and its reciprocal. The square of the number is 'Q' (nearest to the integer) % less than its cube.
Quantity 2: R : The income of Ram is 20% more than that of Gopal and the income of Suresh is 68% less, then the sum of the incomes of Ram & Gopal. Income of Suresh is 'R' % less than the income of Ram.
For Quantity 1, Let the number be= x (x + 1/x) × 0.4 = x – 1/x 0.4x + 0.4/x = x – 1/x 0.6x = 1.4/x x2 = 1.4/0.6 = 7/3 x3 = (7/3)√(7/3) Q = [(7/3)√(7/3) – 7/3]/(7/3) × 100 = [√(7/3) – 1] × 100 = 52.75% For Quantity 2, Let the Income of Gopal be = 100 Rs., The Income of Ram will be = 1.2 × 100 = 120 Rs. Then, Income of Suresh = (100 + 120) × 0.32 = 220 × 0.32 = 70.4 R = (120 – 70.4)/120 × 100 = 41.33% = Q2 Therefore quantity 1 will be greater than quantity 2 Q1 > Q2
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