A B and C share profits in 1:2:3. A retires. What will be the new ratio of B and C if no information is given?

Correct answer: 2:3

The correct answer is Option A, 2:3. A, B and C originally share profits in 1:2:3. When A retires, only B and C remain. No information is given that they will change their relative claims, so the standard rule is that continuing partners retain their old mutual ratio. B's old share is 2 parts and C's old share is 3 parts; removing A's 1 part leaves B:C = 2:3. Option A is correct. Option B, 1:2, incorrectly uses A's old share and B's old share rather than the remaining partners' shares. Option C, 1:3, omits B's correct two-part share and is unsupported. Option D, 3:2, reverses the two remaining partners' proportions. The total old ratio was six parts, but the new ratio need not be written with a total of six; the relative shares of B and C are what matter, and 2:3 already has the correct relationship. Memory cue: on retirement, if no new arrangement is stated, cross out the retiring partner and retain the remaining partners' old ratio.