A and B share profits in the ratio 3:5. C receives a 3/16 share taken equally from A and B. What is the new ratio?

Correct answer: 9:17:6

The direct answer is 9:17:6, so option A is correct. C receives 3/16, taken equally from A and B, so each old partner sacrifices 3/32. Express the old shares with denominator 32: A’s 3/8 becomes 12/32, and B’s 5/8 becomes 20/32. After sacrifice, A receives 12/32−3/32=9/32 and B receives 20/32−3/32=17/32. C receives 3/16=6/32. Hence the new ratio is 9:17:6. The check is 9/32+17/32+6/32=32/32=1, so no profit is missing or counted twice. Option B fails to account for the equal sacrifice and gives C the wrong effective part. Option C reduces the old shares incorrectly and gives an incorrect C component. Option D leaves the old ratio merely scaled and does not subtract the amount transferred to C. A useful warning is that half of 3/16 is 3/32, not 3/16; forgetting this is the main source of error in equal-sacrifice questions.