Question

Kajal and Laura were partners in a firm sharing profits and losses in the ratio of 5:3. They admitted Maddy for \( \frac{1}{4} \)th share in future profits. Maddy brought Rs 8,00,000 as his capital and Rs 4,00,000 as his share of premium for goodwill. Kajal, Laura and Maddy decided to share profits in future in the ratio of 2:1:1. After all adjustments in respect of goodwill, revaluation of assets and liabilities etc. Kajal's capital was Rs 15,00,000 and Laura's capital was Rs 8,00,000. It was agreed that partners' capitals should be in proportion to their new profit sharing ratio taking Maddy's capital as base. The adjustment was made by bringing in or withdrawing the necessary cash as the case may be. The cash brought in by Kajal was:

• A. Rs 1,00,000
• B. Rs 8,00,000
• C. Rs 16,00,000
• D. Rs 12,00,000

Hint:

For capital adjustments based on a new partner's capital: 1. Calculate the total capital of the new firm using the new partner's capital and their profit share. 2. Determine the required capital for each partner by distributing the total capital in the new profit-sharing ratio. 3. Compare the required capital with the existing adjusted capital (after all adjustments like goodwill, revaluation, reserves) for each old partner. 4. The difference indicates cash to be brought in (if required $>$ existing) or withdrawn (if existing $>$ required).

Answer 1

The Correct Option is A

To find the cash brought in by Kajal, we need to understand how the partner's capitals should be adjusted in proportion to their new profit-sharing ratio. Here is the detailed analysis:

1. New Profit-Sharing Ratio: After Maddy joins, Kajal, Laura, and Maddy agree to share profits in the ratio of 2:1:1.
2. Base Capital: Maddy's capital is taken as the base, which is Rs 8,00,000.
3. Capital Based on New Ratio:
   • Total Ratio: 2+1+1 = 4 parts
   • Maddy's Share: Rs 8,00,000 (1 part, as per ratio)
   • Kajal's Required Capital:
     \[ \text{Maddy's Capital} \times \frac{\text{Kajal's Ratio}}{\text{Maddy's Ratio}} = 8,00,000 \times \frac{2}{1} = 16,00,000 \]
   • Laura's Required Capital:
     \[ \text{Maddy's Capital} \times \frac{\text{Laura's Ratio}}{\text{Maddy's Ratio}} = 8,00,000 \times \frac{1}{1} = 8,00,000 \]
4. Adjustment of Actual Capital:
   • Kajal's Actual Capital: Rs 15,00,000
   • Laura's Actual Capital: Rs 8,00,000
5. Adjustment Calculation for Kajal:
   \[ \text{Shortfall} = \text{Required Capital} - \text{Actual Capital} = 16,00,000 - 15,00,000 = 1,00,000 \]

Therefore, Kajal needs to bring in Rs 1,00,000 to adjust her capital to the required level based on the new profit-sharing ratio.

Answer 2

1.Calculate the total capital of the new firm based on Maddy's capital and the new PSR:
Maddy's Capital = Rs 8,00,000 for a \( \frac{1}{4} \) share (New ratio 2:1:1 means Maddy's share is \( \frac{1}{2+1+1} = \frac{1}{4} \)).
Total Capital of the New Firm = Maddy's Capital \( \times \) Reciprocal of his share \[ \text{Total Capital} = 8,00,000 \times \frac{4}{1} = Rs 32,00,000 \] 2. Calculate the required capital for each partner based on the new PSR and total capital:
New PSR = Kajal : Laura : Maddy = 2 : 1 : 1. Kajal's Required Capital = Total Capital \( \times \) Kajal's New Share \[ \text{Kajal's Required Capital} = 32,00,000 \times \frac{2}{4} = Rs 16,00,000 \] Laura's Required Capital = Total Capital \( \times \) Laura's New Share \[ \text{Laura's Required Capital} = 32,00,000 \times \frac{1}{4} = Rs 8,00,000 \] Maddy's Required Capital = Total Capital \( \times \) Maddy's New Share \[ \text{Maddy's Required Capital} = 32,00,000 \times \frac{1}{4} = Rs 8,00,000 (Matches his contribution) \] 3. Compare Kajal's required capital with her existing adjusted capital:
Kajal's Existing Adjusted Capital (after all adjustments for goodwill, revaluation etc.) = Rs 15,00,000.
Kajal's Required Capital = Rs 16,00,000. 4. Calculate the cash to be brought in or withdrawn by Kajal:
Cash Adjustment for Kajal = Required Capital - Existing Adjusted Capital \[ \text{Cash Adjustment for Kajal} = 16,00,000 - 15,00,000 = Rs 1,00,000 \] Since the required capital is more than the existing capital, Kajal needs to bring in cash. Cash brought in by Kajal = Rs 1,00,000.