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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