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 C's share of the profit.
The total profit is Rs. 2,000, split among A, B and C. A gets Rs. 1,000 and B gets Rs. 600, so C gets whatever is left:
\[ 2000 - 1000 - 600 = 400 \]
So C's share of profit is Rs. 400.

Step 2: Recall how profit is shared in a partnership.
When all partners invest for the same length of time, which is the case here since all three are in the business for the full year, profit is split in exactly the same ratio as the investments. So
\[ \text{Investment}_A : \text{Investment}_B : \text{Investment}_C = \text{Share}_A : \text{Share}_B : \text{Share}_C \]

Step 3: Write the profit-share ratio and simplify.
\[ 1000 : 600 : 400 = 5 : 3 : 2 \]
This is the same ratio in which the three investments stand to each other.

Step 4: Use A's known investment to find one ratio unit.
A's investment, Rs. 20,000, corresponds to the 5 part of the ratio. So one ratio unit is worth
\[ \frac{20000}{5} = 4000 \]

Step 5: Find C's investment using its ratio part.
C's part of the ratio is 2, so
\[ \text{Investment}_C = 2 \times 4000 = 8000 \]

Step 6: Why the other options are wrong.
Option (a), Rs. 6,000, and option (d), Rs. 15,000, do not fit the 5:3:2 ratio scaled from A's Rs. 20,000. Option (c), Rs. 12,000, is actually B's investment (the 3 part of the ratio, since \(3\times4000=12000\)), a common mix-up between B and C's shares.

Final Answer:
C's investment is Rs. 8,000. \[ \boxed{\text{Rs. } 8{,}000} \]