Question

A, B and C are three partners in a business. C is the only working partner. C's investment is one-fifth of B's investment and A's investment is twice that of C. If C gets a salary of Rs. 10,500 a month and A gets a profit share of Rs. 1.44 lakh at the end of the year, then what is the total profit?

• A. Rs. 3,96,000
• B. Rs. 4,16,000
• C. Rs. 5,76,000
• D. Rs. 6,20,000
• E. Rs. 7,20,000

Hint:

Find the capital ratio A:B:C = 2:5:1 from the given investment relations, then use A's known profit share of Rs. 1.44 lakh as 2 parts out of 8 to find the whole distributable profit.

Answer 1

The Correct Option is C

Step 1: Set up the investment ratio.
Let C's investment be \(x\). Since C's investment is one-fifth of B's, B's investment is \(5x\). Since A's investment is twice C's, A's investment is \(2x\). So:
$$A:B:C=2x:5x:x=2:5:1$$
The sum of the ratio parts is \(2+5+1=8\).

Step 2: Understand how the profit is distributed.
C is the working partner and is compensated separately for the work through a fixed monthly salary; this salary is paid out of the firm's earnings as an operating cost before the distributable profit is arrived at. The distributable (net) profit that remains, call it \(P\), is shared among all three partners strictly according to their capital contribution, i.e. in the ratio \(2:5:1\), since each of them has money invested in the business.

Step 3: Use A's profit share to find the total distributable profit.
A's share of the ratio is \(2\) parts out of \(8\), so:
$$A's\ share=\frac{2}{8}\times P=1,44,000$$
$$P=1,44,000\times\frac{8}{2}=1,44,000\times4=5,76,000$$

Step 4: Verify with B's and C's shares.
Each part is worth \(5,76,000/8=72,000\). So A gets \(2\times72,000=1,44,000\) (matches the given data exactly), B gets \(5\times72,000=3,60,000\), and C gets \(1\times72,000=72,000\) as an investor's share, in addition to the Rs. 1,26,000 (\(=10,500\times12\)) drawn as annual salary for working in the business.

Step 5: State the total profit.
The total (distributable) profit for the year is Rs. 5,76,000, option (c).

Note on the answer key: A commonly circulated key marks this as option (e) Rs. 7,20,000. Checking that value: if Rs. 7,20,000 (or Rs. 7,20,000 minus the annual salary of Rs. 1,26,000) is split in the 2:5:1 or 2:5 ratio, A's resulting share comes out to Rs. 1,48,500 or Rs. 1,80,000, not the Rs. 1,44,000 stated in the question, so Rs. 7,20,000 does not satisfy the given data under any standard partnership convention. Only Rs. 5,76,000 reproduces A's share of Rs. 1,44,000 exactly, so that is kept as the verified answer here.