Investment Profit Ratio Calculation

The profit earned in a partnership is distributed based on the ratio of the product of the investment amount and the duration for which each partner invested.

Calculate Investment Duration Products

First, calculate the effective investment value for each person by multiplying their investment amount by the number of months they invested:

• Person X's investment product: $₹12,000 \times 12 \text{ months} = ₹144,000$
• Person Y's investment product: $₹18,000 \times 6 \text{ months} = ₹108,000$

Determine Profit Sharing Ratio

The ratio of profit sharing between X and Y is the ratio of their investment products:

Ratio X : Y = $₹144,000 : ₹108,000$

Simplify the ratio:

Ratio X : Y = $144 : 108$

Divide both sides by their greatest common divisor (36,000 or simplify step-by-step):

Divide by 12: $12 : 9$

Divide by 3: $4 : 3$

So, the profit is shared in the ratio 4:3.

Calculate X's Share of Profit

The total profit is ₹25,200. The ratio has a total of $4 + 3 = 7$ parts.

X's share is calculated as:

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

X's Share = $\frac{4}{7} \times ₹25,200$

Calculation:

X's Share = $4 \times \frac{₹25,200}{7}$

X's Share = $4 \times ₹3,600$

X's Share = $₹14,400$