Multiple choice

Passage

Directions: The question is followed by two statements I and II. You have to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

X, Y and Z invested a sum of money in a partnership firm. X invested Rs. 45,000 more than what Y invested. Z invested Rs. 75,000. Money was invested by X, Y and Z for 10, 5 and 6 months, respectively. Find the amount invested by X. I. The profit sharing ratio was 6 : 1 : 4. II. The difference between X's share and Y's share of profit was Rs. 70,000.

  1. The question can be answered by using statement I alone but cannot be answered using the other statement alone.

  2. The question can be answered by using statement II alone but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both of the statements together but cannot be answered using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
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A Correct answer
AI explanation

Using statement I, we have the known investment amounts as (Y + 45000) for X, Y for Y, and 75000 for Z. The time periods are 10, 5 and 6 months. The profit ratio equals the ratio of investment multiplied by time, so (10Y + 450000) : 5Y : 450000 equals 6 : 1 : 4. By equating 5Y to 1 and 450000 to 4, the multiplier is 112500, making 5Y equal to 112500 and Y equal to 22500. Since Y is found, X is 22500 + 45000 = 67500, which means statement I alone is sufficient. Statement II only provides the difference between profit shares, which yields the equation 5Y + 450000 = 70000k and 5Y = 10000k, leading to 400000 = 60000k and giving multiple possible values for Y and X, meaning statement II alone is not sufficient.

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