A and B share profits in the ratio 4:3. C is admitted for a 1/7 share, sacrificed by A and B in their old ratio. What is the new ratio?

Correct answer: A:B:C = 24:18:7

The direct answer is A:B:C=24:18:7, so option A is correct. C receives 1/7 of the total profit, leaving 6/7 for A and B together. The statement says that A and B sacrifice in their old ratio 4:3, so the remaining 6/7 must be divided between them in the fractions 4/7 and 3/7. A’s new share is (6/7)×(4/7)=24/49. B’s new share is (6/7)×(3/7)=18/49. C’s share is 1/7=7/49. Removing the common denominator 49 gives the ratio 24:18:7. The parts add to 24+18+7=49, confirming that the complete profit is distributed. Option B fails to reduce A and B’s shares after C enters. Option C uses an incorrect reduction, and option D simply scales the old ratio without correctly allocating C’s share. A useful warning is to distinguish the old ratio from the new ratio: the old ratio determines how the remaining profit is shared, but it is not itself the final ratio.