Calculating Arjun's Profit Share
This problem involves calculating a partner's share of profit based on their investment and the duration of their investment in a business.
Step 1: Determine Total Profit
We are given that 20% of the total profit is ₹30,600. To find the total profit, we can set up the following calculation:
Let the Total Profit be \(P\).
\( 0.20 \times P = ₹30,600 \)
\( P = \frac{₹30,600}{0.20} \)
\( P = ₹1,53,000 \)
The total profit at the end of the year is ₹1,53,000.
Step 2: Calculate Profit Sharing Ratio
The profit is shared based on the product of the investment amount and the time period (in months) for which the investment was made. This is often referred to as the 'capital invested ratio' adjusted for time.
- Karan's investment product: \(₹45,000 \times 4 \text{ months} = 1,80,000\)
- Arjun's investment product: \(₹50,000 \times 10 \text{ months} = 5,00,000\)
The ratio of profit sharing between Karan and Arjun is:
\( \text{Karan : Arjun} = 1,80,000 : 5,00,000 \)
Simplifying the ratio by dividing both sides by 10,000:
\( \text{Karan : Arjun} = 18 : 50 \)
Further simplifying by dividing by 2:
\( \text{Karan : Arjun} = 9 : 25 \)
Step 3: Calculate Arjun's Profit Share
The total parts in the ratio are \(9 + 25 = 34\). Arjun's share will be his part of the ratio (25) divided by the total parts (34), multiplied by the total profit.
\( \text{Arjun's Share} = \left( \frac{\text{Arjun's Ratio Part}}{\text{Total Ratio Parts}} \right) \times \text{Total Profit} \)
\( \text{Arjun's Share} = \left( \frac{25}{34} \right) \times ₹1,53,000 \)
\( \text{Arjun's Share} = 25 \times \frac{₹1,53,000}{34} \)
\( \text{Arjun's Share} = 25 \times ₹4,500 \)
\( \text{Arjun's Share} = ₹1,12,500 \)
Therefore, Arjun's share of the profit is ₹1,12,500.
Similar Questions
- A and B start a business by investing ₹40,000 and ₹60,000, respectively. At the end of the year, they earn a profit of ₹20,000. How much profit will A receive?
- Two partners M and N buy a car. M pays his share of $\frac{3}{7}$th of the total cost of the car. M pays ₹ 31,540 less than N. What is the cost of the car?
Important Questions from Partnership
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)?
Sumit, Ravi and Puneet invest Rs. 45000, Rs. 81000 and Rs. 90000 respectively to start a business. At the end of the year the total profit is Rs. 4800. 30% of the total profit gives in charity and rest is divided among them. What will be the share of Sumit?
A sum of ₹ 159250 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3. The share (in ₹) of A is:
A and B start a business by investing Rs. 1,00,000 and Rs. 1,50,000 respectively. Find the respective share of each out of a total profit of Rs. 24, 000.
Two partners A and B have started business with the capitals of Rs. 6,000 and Rs. 8,000 respectively. If they made profit of Rs. 5,600 then the share (in Rs.) of A is:
