A and B share profits in the ratio 6:5. C is admitted as a partner with a \(\frac{2}{11}\) share of the profits. The remaining profit will be shared by A and B in the ratio 4:3. What will be A’s new profit-sharing share?

Correct answer: \(\frac{36}{77}\)

After C receives \(\frac{2}{11}\) of the profit, the share remaining for A and B is \(1-\frac{2}{11}=\frac{9}{11}\). A receives \(\frac{4}{7}\) of this remaining profit because A and B share it in the ratio 4:3. Therefore, A’s new share is \(\frac{9}{11}\times\frac{4}{7}=\frac{36}{77}\). The value \(\frac{4}{7}\) represents A’s share of the remaining profit only, not of the total profit. In such questions, first calculate the balance profit and then multiply it by the relevant part of the new ratio.