X and Y are partners in a business. X contributed1/3 of the capital for 9 months and Y received2/5 of the profit. For how long was Y's money used in the business ?a)2 monthsb)3 monthsc)4 mo0nthsd)5 monthsCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

To solve this problem, we need to understand the information provided and use it to calculate the duration for which Y's money was used in the business.

Given information:
- X contributed 1/3 of the capital.
- X's capital was used for 9 months.
- Y received 2/5 of the profit.

Let's break down the problem into smaller steps:

Step 1: Calculate the duration for which X's money was used
X contributed 1/3 of the capital, so the remaining 2/3 of the capital must have been contributed by Y. Since X's capital was used for 9 months, we can assume that Y's capital was used for the remaining duration.

Step 2: Calculate the duration for which Y's money was used
To find the duration for which Y's money was used, we need to calculate the total duration of the business.

Let's assume the total duration of the business is 'T' months.

Since X's money was used for 9 months, Y's money must have been used for T - 9 months.

Step 3: Calculate Y's share of the profit
Y received 2/5 of the profit.

Step 4: Equate the profit shares of X and Y
Since X and Y are partners, their profit shares should be equal.

Y's share of the profit = (2/5) * Total Profit

X's share of the profit = (1/3) * Total Profit

Since their profit shares are equal, we can set up the equation:

(2/5) * Total Profit = (1/3) * Total Profit

Step 5: Solve the equation for T
By canceling out the Total Profit on both sides, we can solve the equation:

2/5 = 1/3

Cross-multiplying, we get:

6 = 5

This is not possible, so there must be an error in the given information.

Therefore, it is not possible to determine the duration for which Y's money was used based on the information provided.

The correct answer cannot be determined based on the given information.

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