The question consists of two statements numbered “I

Solution

ATQ, Let Aman and Bittu can be defined as A and B.

So, A and B initially invest Rs. 4x and Rs. 3x, respectively. Let their additional investments be Rs. 3y for A and Rs. y for B. Then, the profit-sharing ratio becomes: A : B = (4x + 4x + 3y) : (3x + 3x + y) = (8x + 3y) : (6x + y) Statement I: As per the given information: (8x + 3y)/(14x + 4y) = 1530/2448 ⇒ (8x + 3y)/(14x + 4y) = 5/8 ⇒ Cross-multiplying: 64x + 24y = 70x + 20y ⇒ Simplifying: 6x = 4y ⇒ So, 3x = 2y Since we have two variables, the equation cannot be solved uniquely. Hence, Statement I alone is insufficient to determine the required values. Statement II: As per the question: (6x + y)/(14x + 4y) = 1800/4800 ⇒ (6x + y)/(14x + 4y) = 3/8 ⇒ Cross-multiplying: 48x + 8y = 42x + 12y ⇒ Simplifying: 6x = 4y ⇒ So, 3x = 2y Again, we have two unknowns, and the equation can't be solved. Therefore, Statement II alone is insufficient. Combining Statements I and II: Since both statements lead to the same equation (3x = 2y), we still cannot determine unique values for x and y. Therefore, the data in both Statements I and II together are not sufficient to answer the question.