Question

Radhika, Mehar, and Shubha were partners in a firm sharing profits and losses in the ratio of 9:8:7. If Radhika's share of profit at the end of the year amounted to Rs 5,40,000, Shubha's share of profit will be:

• A. Rs 5,40,000
• B. Rs 4,80,000
• C. Rs 60,000
• D. Rs 4,20,000

Hint:

If you know the profit share of one partner and the profit-sharing ratio, you can easily calculate the profit share of another partner. First, find the value of one 'part' of the ratio by dividing the known share by the number of parts it represents. Then, multiply this value by the number of parts corresponding to the desired partner.

Answer 1

The Correct Option is D

To solve the problem, we need to determine Shubha's share of profit based on the given ratio of profit sharing and Radhika's share of profit.

The profit-sharing ratio among Radhika, Mehar, and Shubha is given as 9:8:7.

Let's assign these ratios to R, M, and S respectively. Hence, Radhika's share = 9 parts, Mehar's share = 8 parts, Shubha's share = 7 parts.

We also know Radhika's share of profit at the end of the year is Rs 5,40,000.

Using the profit ratio, we can set the equation:

Total ratio sum = 9 + 8 + 7 = 24 parts.

Now, Radhika's share = \( \frac{9}{24} \) of Total Profit.

Since \( \frac{9}{24} \) of Total Profit = Rs 5,40,000, we can solve for the Total Profit:

Let Total Profit = P, then \( \frac{9}{24}P = 5,40,000 \).

Solving for P:

\[ P = \frac{5,40,000 \times 24}{9} \]

\[ P = \frac{1,29,60,000}{9} \]

\[ P = 14,40,000 \]

Now, let's calculate Shubha's share:

Shubha's share = \( \frac{7}{24} \) of Total Profit.

\[ \text{Shubha's share} = \frac{7}{24} \times 14,40,000 \]

\[ = \frac{1,00,80,000}{24} \]

\[ = 4,20,000 \]

Thus, Shubha's share of profit will be Rs 4,20,000.

Answer 2

The profit-sharing ratio of Radhika, Mehar, and Shubha is 9:8:7.
Total parts in the ratio = \( 9 + 8 + 7 = 24 \) parts.
- Radhika's share = \( \frac{9}{24} \) of the total profit.
- Mehar's share = \( \frac{8}{24} \) of the total profit.
- Shubha's share = \( \frac{7}{24} \) of the total profit. We are given that Radhika's share of profit = Rs 5,40,000.
Let the total profit of the firm be \( P \). From the given information: \[ \text{Radhika's share} = \frac{9}{24} \times P = 5,40,000 \] Now, let's calculate the total profit \( P \): \[ P = 5,40,000 \times \frac{24}{9} = 60,000 \times 24 = Rs 14,40,000 \] Next, we calculate Shubha's share of the profit: \[ \text{Shubha's share} = \frac{7}{24} \times P = \frac{7}{24} \times 14,40,000 \] \[ \text{Shubha's share} = 7 \times \frac{14,40,000}{24} = 7 \times 60,000 = Rs 4,20,000 \] Alternatively, we can solve directly using the ratio method:
Radhika's share corresponds to 9 parts = Rs 5,40,000.
Value of 1 part = \( \frac{5,40,000}{9} = Rs 60,000 \).
Shubha's share corresponds to 7 parts, so: \[ \text{Shubha's share} = 7 \times 60,000 = Rs 4,20,000 \] Thus, Shubha's share of the profit is Rs 4,20,000.