The ratio of income of Rakesh and Sanju is 8 : 9 respectively. If Rakesh's income is increased by 50% and Sanju's income is decreased by 25%, the new ratio of their income becomes 16 : 9. What is Rakesh's income?

Let Rakesh's income = 8x and Sanju's income = 9x. After changes: Rakesh's new income = 8x + 50% of 8x = 12x. Sanju's new income = 9x - 25% of 9x = 6.75x. New ratio = 12x : 6.75x = 12 : 6.75 = 16 : 9 (when simplified). This ratio holds true regardless of x's value. Since we cannot determine x uniquely from the given information (any value of x would satisfy the ratio condition), Rakesh's actual income cannot be determined.