In a business, P invests ₹2,00,000 for 8 months, Q invests ₹1,50,000 for 9 months and R invests ₹1,20,000 for some complete months. After a year, out of the profit, R gets a higher profit amount than Q but less than P. If R gets ₹72,000 as profit, then the profit of P is ₹_______.
80,000
Profit is proportional to (investment × time). P: \(2{,}00{,}000\times8=16{,}00{,}000\); Q: \(1{,}50{,}000\times9=13{,}50{,}000\); R: \(1{,}20{,}000\times m\).
Let k be profit per unit investment-month. R's profit: \(1{,}20{,}000\times m\times k = 72{,}000\).
Since R's profit must exceed Q's but stay below P's, testing m=12 (the maximum whole months in a year) gives \(k = \dfrac{72{,}000}{1{,}20{,}000\times12} = 0.05\).
Q's profit: \(13{,}50{,}000\times0.05 = 67{,}500\), which is indeed less than R's ₹72,000, confirming m=12.
P's profit: \(16{,}00{,}000\times0.05 = 80{,}000\).
Hence, the profit of P is ₹80,000.
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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.
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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?
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