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.

Quantity I:

Let the number be n (> 1).

Given:

n − 1/n = 0.4 × (n + 1/n)

Multiply both sides by n:

n² − 1 = 0.4(n² + 1)

n² − 1 = 0.4n² + 0.4

n² − 0.4n² = 1 + 0.4

0.6n² = 1.4

n² = 1.4 / 0.6 = 7/3

So, n = √(7/3)

Square = n²

Cube = n³

Square is X% less than cube:

X = [(cube − square) / cube] × 100

= [(n³ − n²) / n³] × 100

= (1 − 1/n) × 100

1/n = √(3/7) ≈ 0.6546

So, X ≈ (1 − 0.6546) × 100 ≈ 34.54 ≈ 35 (nearest integer)

Quantity I, X = 35 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