A and B share profits in the ratio 2:3. C is admitted for a 1/5 share, taken from A and B in the sacrificing ratio 1:1. What is the new ratio?

Correct answer: 3:5:2

The mathematically correct new ratio is 3:5:2, so option A is correct after correcting the original option text. C receives 1/5, and the sacrifice is equal, so A and B each give up half of 1/5, which is 1/10. A’s old share is 2/5=4/10; after sacrifice it becomes 4/10−1/10=3/10. B’s old share is 3/5=6/10; after sacrifice it becomes 6/10−1/10=5/10. C receives 1/5=2/10. Therefore the new shares are 3/10, 5/10, and 2/10, giving 3:5:2. Their total is 3+5+2=10, so the shares add to the whole profit. Option B leaves the old shares unchanged and gives C an incorrectly scaled share. Option C does not subtract equal sacrifices correctly, and option D reverses the old partners’ relative shares. The key warning is that an equal sacrifice means equal fractions are subtracted, not equal proportions of the old shares.