A and B share profits in (7:8). C is admitted for (1/3) share. A and B's new mutual ratio is (3:2). What is A's sacrifice?

Correct answer: (1/15)

The direct answer is A: A’s sacrifice is \(1/15\). The old ratio 7:8 means A originally had \(7/15\), while B had \(8/15\). C receives \(1/3\), so the two old partners together retain \(1-1/3=2/3\). Their new mutual ratio is 3:2, whose total is 5; therefore A’s new share is \(2/3\times3/5=2/5\). Sacrifice means old share minus new share: \(7/15-2/5=7/15-6/15=1/15\). Option A is correct. Option B, \(7/15\), is A’s old share, not sacrifice. Option C, \(2/15\), is not the difference. Option D says gain, but A gives up part of his share, so it is sacrifice, not gain. Remember: sacrifice = old share − new share.