Atul, Beena, and Sita were partners in a firm sharing profits and losses in the ratio of 8 : 7 : 5. Damini was admitted as a new partner for $\frac{1{5}$ share in the profits, which she acquired entirely from Atul. The new profit-sharing ratio after Damini’s admission 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

Atul's total share before Damini's admission was 20 parts (8 + 7 + 5). Damini obtained 1/5 of Atul's share, which is 4 parts (1/5 * 20). Atul's updated share is 7 parts (8 - 4). Beena and Sita's shares remain 7 and 5 parts, respectively. Damini's share is 4 parts. The revised profit-sharing ratio is 7:7:5:1.

Atul, Beena, and Sita were partners in a firm sharing profits and losses in the ratio of 8 : 7 : 5. Damini was admitted as a new partner for $\frac{1{5}$ share in the profits, which she acquired entirely from Atul. The new profit-sharing ratio after Damini’s admission will be:}

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The Correct Option is A

Solution and Explanation

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