Profit Sharing Calculation

The profit in a business partnership is shared among partners in proportion to their capital investment. Here, partners A and B invested different amounts, and we need to find B's share of the total profit.

Calculate Capital Ratio

Partner A invested ₹12,000.

Partner B invested ₹18,000.

The ratio of their capitals is:

$ \text{A's Capital : B's Capital} = ₹12,000 : ₹18,000 $

Simplifying this ratio by dividing both amounts by their greatest common divisor (₹6,000):

$ \frac{12000}{6000} : \frac{18000}{6000} = 2 : 3 $

So, the ratio of capitals A : B is 2 : 3.

Determine Total Parts and B's Share

The total number of parts in the ratio is the sum of the individual ratios:

$ \text{Total Parts} = 2 + 3 = 5 $

The total profit made at the end of the year is ₹1,800.

B's share of the profit is calculated using B's ratio part out of the total parts, multiplied by the total profit:

$ \text{B's Profit Share} = \left( \frac{\text{B's Ratio Part}}{\text{Total Parts}} \right) \times \text{Total Profit} $

Substituting the values:

$ \text{B's Profit Share} = \left( \frac{3}{5} \right) \times ₹1,800 $

Now, perform the calculation:

$ \text{B's Profit Share} = 3 \times \left( \frac{₹1,800}{5} \right) $

$ \text{B's Profit Share} = 3 \times ₹360 $

$ \text{B's Profit Share} = ₹1,080 $

Therefore, the profit share of B is ₹1,080.