Understanding the Investment and Profit Sharing Problem
This problem involves calculating the difference between the investments made by two partners, Kushal and Brijesh, based on their total investment and how they shared the profit at the end of the year.
Step-by-Step Solution
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Calculate Kushal's Profit Share:
We know the total profit and Brijesh's share. Kushal's share is the remaining amount.
Kushal's Profit = Total Profit - Brijesh's Profit
Kushal's Profit = ₹12,000 - ₹5,700 = ₹6,300
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Determine the Ratio of Profits:
The profit is shared between partners in the same ratio as their investments. First, let's find the ratio of Kushal's profit to Brijesh's profit.
Ratio = Kushal's Profit : Brijesh's Profit
Ratio = ₹6,300 : ₹5,700
To simplify the ratio, divide both numbers by their greatest common divisor. We can start by dividing by 100:
Ratio = 63 : 57
Now, divide both by 3:
Ratio = 21 : 19
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Relate Profit Ratio to Investment Ratio:
Since profits are shared based on investments, the ratio of their investments is the same as the ratio of their profits.
Kushal's Investment : Brijesh's Investment = 21 : 19
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Calculate the Total Ratio Parts:
Add the parts of the ratio to find the total number of parts representing the whole investment.
Total Parts = 21 + 19 = 40 parts
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Calculate the Value of One Investment Ratio Part:
The total investment of ₹37,100 is divided into these 40 parts.
Value of 1 Part = Total Investment / Total Parts
Value of 1 Part = ₹37,100 / 40
Value of 1 Part = ₹927.5
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Calculate the Difference in Investments:
The difference in their investments corresponds to the difference in their ratio parts.
Difference in Ratio Parts = Kushal's Parts - Brijesh's Parts
Difference in Ratio Parts = 21 - 19 = 2 parts
Now, multiply the difference in parts by the value of one part:
Difference in Investment = Difference in Ratio Parts × Value of 1 Part
Difference in Investment = 2 × ₹927.5
Difference in Investment = ₹1,855
Conclusion
The difference between Kushal's and Brijesh's investments was ₹1,855.
Important Questions from Partnership
- M and N start a business. M invests ₹68,000 more than N for 4 months and N invests for 7 months. M's share is ₹856 more than that of N, out of a total profit of ₹6,848. Find the capital contributed by M.
- Rekha, Sanjay, and Poonam invest ₹1,320, ₹1,170, and ₹1,660, respectively, to start a business. If the profit at the end of the year is ₹1,010, then what is the share of Poonam in the profit?
M and N start a business. M invests ₹79,000 more than N for 7 months and N invests for 6 months. M's share is ₹745 more than that of N, out of a total profit of ₹6,705. Find the capital contributed by M.
- Ritik and Sanjay together invested ₹79,200 in a business. At the end of the year, out of a total profit of ₹16,500, Sanjay's share was ₹3,600. What was the difference between their investments?
- P, Q and R invested a sum in the ratio of 34: 75: 6, respectively. If they earned a total profit of ₹3,600 at the end of the year, what is the difference between the shares of Q and R?
