The correct answer is: C. Sacrificing ratio.
The sacrificing ratio is the ratio in which the old partners agree to sacrifice their share of the profit in order to admit a new partner. In this case, Z is admitted for 14 shares in the profit, which means that he is taking 14/(14+X+Y) = 14/(14+2X) of the profit. The old partners, X and Y, must therefore agree to sacrifice their share of the profit so that Z can have his 14 shares. The sacrificing ratio is the ratio in which they agree to do this.
The old profit-sharing ratio is the ratio in which the old partners shared the profit before Z was admitted. This ratio is not relevant to the calculation of the sacrificing ratio.
The new profit-sharing ratio is the ratio in which the old and new partners will share the profit after Z is admitted. This ratio is calculated after the sacrificing ratio has been determined.
The capital ratio is the ratio in which the old partners’ capitals are related to each other. This ratio is also not relevant to the calculation of the sacrificing ratio.