Nicku, Mala, and Ritu were partners in a firm sharing profits in the ratio of \( 5 : 3 : 2 \). Nicku died on 30\textsuperscript{th September, 2023. The deceased partner was entitled to his share of profit up to the date of death, which was to be calculated on the basis of the previous year’s profit. The previous year’s profit was ₹ 80,000. Nicku’s share of profit will be:}

Question

Let \(y=y(x)\) be the solution of the differential equation \[ x\frac{dy}{dx}=y-x^2\cot x,\quad x\in(0,\pi) \] If \(y\!\left(\frac{\pi}{2}\right)=\frac{\pi^2}{2}\), then \[ 6y\!\left(\frac{\pi}{6}\right)-8y\!\left(\frac{\pi}{4}\right) \] is equal to:

Answer 1

Nicku's profit share is determined by the following formula: \[\text{Share of Profit} = \text{Previous Year’s Profit} \times \frac{\text{Share Ratio}}{\text{Total Ratio}} \times \frac{\text{Months Active}}{12}.\] When values are substituted, the calculation is: \[\text{Share of Profit} = ₹ 80,000 \times \frac{5}{10} \times \frac{6}{12} = ₹ 20,000.\]

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The Correct Option is B

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