Each of the following questions consists of 3 statements A, B, and C. You have to determine which of the following statement/statements are necessary to answer the question:

A, B, and C entered into a partnership. The profit earned in the business is proportional to the investment and the duration of investment. What is the profit of B if all of them invested the amount for one year and the total profit is Rs. $x$?

Statements:

A. A invested Rs. 1500 more than C.

B. A invested 2 times more than B. C invested 3 times more than A.

C. B invested 200\% more than A and 100\% less than C.

Question

Each of the following questions consists of 3 statements A, B, and C. You have to determine which of the following statement/statements are necessary to answer the question:

A, B, and C entered into a partnership. The profit earned in the business is proportional to the investment and the duration of investment. What is the profit of B if all of them invested the amount for one year and the total profit is Rs. $x$?

Statements:

A. A invested Rs. 1500 more than C.

B. A invested 2 times more than B. C invested 3 times more than A.

C. B invested 200\% more than A and 100\% less than C.

Accepted Answer

**Solution:**

1. The profit share depends on the product of investment and time. Since the time period is the same (one year) for all, the profit share is directly proportional to the investment amounts.

2. We need to find the profit of B, which requires knowing the ratio of investments of A, B, and C.

3. Statement A alone gives a difference between A and C's investments but does not relate B's investment, so it is insufficient.

4. Statement B says A invested twice as much as B, and C invested three times as much as A. From this, we can find the ratio:

- Let B's investment be $b$.
   - Then A's investment = $2b$.
   - C's investment = $3 	imes 2b = 6b$.

So, the ratio A:B:C = $2b : b : 6b = 2 : 1 : 6$.

5. Statement C says B invested 200\% more than A (which means B = A + 2A = 3A), and B invested 100\% less than C (which means B = C - C = 0, but this is likely a misinterpretation; assuming it means B is half of C, or 100\% less is ambiguous). However, if interpreted as B invested 100\% less than C, it implies B = 0, which is not possible. Assuming it means B invested half of C, then:

- B = 3A
   - B = 0.5C

From this, C = 2B = 2 	imes 3A = 6A.

So, ratio A:B:C = A : 3A : 6A = 1 : 3 : 6.

6. Both statements B and C independently provide a ratio of investments, allowing calculation of B's share of profit.

7. Therefore, either statement B alone or statement C alone is sufficient to find B's profit share.

**Answer:** Either B or C alone

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