Question

A, B and C start a business in which A's investment is Rs. 20,000. At the end of the year, out of a total profit of Rs. 2,000, A's share is Rs. 1,000 and B's share is Rs. 600. Find the investment of C.

• A. Rs. 6,000
• B. Rs. 8,000
• C. Rs. 12,000
• D. Rs. 15,000

Hint:

Profit shares split in the same ratio as investments here; find C's share first, then scale.

Answer 1

The Correct Option is B

Step 1: Find the fixed ratio between investment and profit share.
Since all three partners invested for the same one-year period, the ratio of any partner's investment to their profit share stays the same across all partners. Using A's numbers:
\[ \frac{\text{Investment}_A}{\text{Share}_A} = \frac{20000}{1000} = 20 \]
So every partner's investment is exactly 20 times their profit share.

Step 2: Find C's profit share.
Total profit is Rs. 2,000. A's share is Rs. 1,000 and B's share is Rs. 600, so C's share is
\[ 2000 - 1000 - 600 = 400 \]

Step 3: Apply the constant multiplier to C's share.
\[ \text{Investment}_C = 20 \times 400 = 8000 \]

Step 4: Check this multiplier against B as well.
If the rule is correct, B's investment should also be 20 times B's share: $20 \times 600 = 12000$. Added up, the three investments are $20000+12000+8000=40000$, and the three shares are $1000+600+400=2000$, and indeed $40000/2000=20$, the same multiplier throughout, which confirms the method is consistent.

Final Answer:
Using the constant investment-to-share multiplier also gives C's investment as Rs. 8,000. \[ \boxed{\text{Rs. } 8{,}000} \]