Read the following passage and answer the questions

A Solid Partnership

A, V and T were partners of a law firm sharing profits in the ratio of 5:3:2. Their partnership deed provided the following:

(i) Interest on partners' capital @ 5% p.a.

(ii) A guaranteed that he would earn a minimum annual fee of Rs. 6,00,000 for the firm.

(iii) T was guaranteed a profit of Rs. 2,50,000 (excluding interest on capital) and any deficiency on account of this was to be borne by A and V in the ratio of 2:3.

During the year ending March 31, 2019, A earned a fee of Rs. 3,20,000 and net profits earned by the firm were Rs. 8,60,000. Partner's capital on April 01, 2018 were A - Rs. 3,00,000; V - Rs. 3,00,000 and T- Rs. 2,00,000.

Q.) What is the amount of T's deficiency in profits?

The correct option is Rs. 30,000.

Here is the detailed, step-by-step explanation and calculation of T's deficiency in profits:

Step 1: Calculate the deficiency in the fee guaranteed by Partner A
Partner A guaranteed that he would earn a minimum annual fee of Rs. 6,00,000 for the firm. However, he actually earned Rs. 3,20,000. The deficiency to be recovered from A's Capital Account and credited to the firm is calculated as:

$\text{A's Deficiency in Fee}=\text{Guaranteed Fee}-\text{Actual Fee Earned}$

$\text{A's Deficiency in Fee}=\text{Rs. 6,00,000}-\text{Rs. 3,20,000}=\text{Rs. 2,80,000}$

Step 2: Determine the total profit before appropriations
The net profit earned by the firm during the year was Rs. 8,60,000. Adding A's guaranteed fee deficiency, we get the total adjusted profit available for distribution:

$\text{Total Adjusted Profit}=\text{Net Profits}+\text{A's Deficiency in Fee}$

$\text{Total Adjusted Profit}=\text{Rs. 8,60,000}+\text{Rs. 2,80,000}=\text{Rs. 11,40,000}$

Step 3: Calculate the Interest on Partners' Capital
Interest on capital is provided at 5% p.a. on the capital balances as of April 01, 2018:
- Interest on A's Capital: Rs. 3,00,000 × 5% = Rs. 15,000
- Interest on V's Capital: Rs. 3,00,000 × 5% = Rs. 15,000
- Interest on T's Capital: Rs. 2,00,000 × 5% = Rs. 10,000

$\text{Total Interest on Capital}=\text{Rs. 15,000}+\text{Rs. 15,000}+\text{Rs. 10,000}=\text{Rs. 40,000}$

Step 4: Calculate the Divisible Profit
The divisible profit is the profit remaining after deducting the total interest on capital from the adjusted total profit:

$\text{Divisible Profit}=\text{Total Adjusted Profit}-\text{Total Interest on Capital}$

$\text{Divisible Profit}=\text{Rs. 11,40,000}-\text{Rs. 40,000}=\text{Rs. 11,00,000}$

Step 5: Share the Divisible Profit in the Ratio of 5:3:2
The divisible profit is shared among A, V, and T. We calculate T's actual share of the divisible profit (excluding interest on capital) using his profit ratio (2/10):

$\text{T's Share of Profit}=\text{Rs. 11,00,000}\times \frac{2}{10}=\text{Rs. 2,20,000}$

Step 6: Calculate T's Deficiency
T was guaranteed a minimum profit of Rs. 2,50,000 (excluding interest on capital). Comparing T's guaranteed profit with his actual share of the profit:

$\text{Deficiency in T's Share}=\text{Guaranteed Profit}-\text{Actual Share of Profit}$

$\text{Deficiency in T's Share}=\text{Rs. 2,50,000}-\text{Rs. 2,20,000}=\text{Rs. 30,000}$

Thus, the amount of T's deficiency in profits is Rs. 30,000.