Multiple choice

Directions: The item given below consists of a question and two statements, numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and mark accordingly. A and B started a business. A invested Rs. X and B invested Rs. 1.5X. Six months after the start of business, C joined them with an investment of Rs. 5000. If the total annual profit was Rs. 6000, what was A's share of the same? I. C's share of the total annual profit was Rs. 2000. II. X = 2000

  1. The data in both the statements I and II together is necessary to answer the question.

  2. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  3. The data in both the statements I and II together is not sufficient to answer the question.

  4. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  5. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
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B Correct answer
Explanation

Profit sharing ratio depends on investment and time. A:B:C = (X*12):(1.5X*12):(5000*6) = 12X : 18X : 30000. Total profit = 6000. If we know C's share (2000), we know C's proportion of the total, which allows solving for X. If we know X=2000, we can calculate the ratio and thus A's share. Both are sufficient independently.

AI explanation

The ratio of profit shares of A, B, and C is (X * 12) : (1.5X * 12) : (5000 * 6), which simplifies to 12X : 18X : 30000. Using statement I, since C's share is Rs. 2000 out of the total profit of Rs. 6000, the combined share of A and B is Rs. 4000; thus 30X corresponds to 4000, allowing you to calculate A's share of 12X. Using statement II, if X equals 2000, the ratio becomes 24000 : 36000 : 30000, making A's share 6000 * (24 / 90). Therefore, either statement alone is sufficient to answer the question.

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