Question
The question consists of two statements numbered “I
and II” given below it. You have to decide whether the data provided in the statements are suicient to answer the question. Aman and Bittu entered into a business partnership, contributing initially in the ratio 4:3. After one year, they infused additional capital in the ratio 3:1. Determine Aman’s initial investment. Statement I: Out of a total profit of Rs. 2,448, Aman’s share is Rs. 1,530. Statement II: Out of a total profit of Rs. 4,800, Bittu’s share is Rs. 1,800.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.
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