A, B and C entered into a partnership. After eight months, B and C left the business. Find the total profit at the end of year.

Given statements:

A. Annual profit of B is Rs. 400 more than that of A and Rs. 200 more than that of C.

B. Amount invested by C is 50% of total amount invested by A & B together.

C. Ratio of profit share of C and that of A and B together is 3 : 8.

Which of the following is correct?

(a) Either A & B together or B & C together

(b) Either A & C or B & C together

(c) Any two of them

(d) None of the given statements can answer the question

(e) Either A & C together or A & B together

Question

A, B and C entered into a partnership. After eight months, B and C left the business. Find the total profit at the end of year.

Given statements:

A. Annual profit of B is Rs. 400 more than that of A and Rs. 200 more than that of C.

B. Amount invested by C is 50% of total amount invested by A & B together.

C. Ratio of profit share of C and that of A and B together is 3 : 8.

Which of the following is correct?

(a) Either A & B together or B & C together

(b) Either A & C or B & C together

(c) Any two of them

(d) None of the given statements can answer the question

(e) Either A & C together or A & B together

Accepted Answer

**Solution:**

1. Given the ratio of time invested by A, B, and C is 12 : 8 : 8, which simplifies to 3 : 2 : 2.

2. From statement A:
   - Let profit of A = $x$.
   - Then profit of B = $x + 400$.
   - Profit of C = $x + 200$.

3. From statement B:
   - Let amount invested by A & B together = $2P$.
   - Amount invested by C = $3P$ (since C's investment is 50% of A & B together, $C = 0.5 	imes (A+B)$, but the problem states C is 50% of total invested by A & B together, so $C = 0.5 	imes (A+B)$, which means $C = 0.5 	imes 2P = P$, but the solution states $3P$, so this is inconsistent. This inconsistency shows the problem in using the statements together.)

4. From statement C:
   - Ratio of profit share of C and that of A and B together is 3 : 8.

5. There are two variables (profit and investment amounts) and three statements, but none of the statements alone or in pairs provide enough information to find the total profit at the end of the year.

6. Hence, none of the given statements or their combinations can answer the question.

**Answer:** (d) None of the given statements can answer the question

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