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 = $₹14,400$
Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
