Question

S and T are partners in a firm sharing profits in the ratio of 3:2. They admit U as a new partner. S surrenders \(\frac{1}{4}\) of his share and T surrenders 1/3 of his share in favour of U. Sacrificing ratio of S and T will be:
Choose the correct answer from the options given below:

• A. 9:8
• B. 1:1
• C. 3:2
• D. 3:4

Answer 1

The Correct Option is A

To find the sacrificing ratio of S and T, we first need to calculate their original profit shares and the shares they surrender. 1. Original Shares: - S's share = $\frac{3}{5}$ (since 3 + 2 = 5) - T's share = $\frac{2}{5}$ 2. Shares Surrendered: - S surrenders $\frac{1}{4}$ of his share: \[ \text{S's surrender} = \frac{1}{4} \times \frac{3}{5} = \frac{3}{20} \] - T surrenders $\frac{1}{3}$ of his share: \[ \text{T's surrender} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} \] 3. Finding the Sacrificing Ratio: To find the sacrificing ratio, we need a common denominator. The LCM of 20 and 15 is 60. - Convert S's surrender: \[ \frac{3}{20} = \frac{9}{60} \] - Convert T's surrender: \[ \frac{2}{15} = \frac{8}{60} \] 4. Sacrificing Ratio: The sacrificing ratio of S and T: \[ \text{Sacrificing ratio} = \frac{\text{S's surrender}}{\text{T's surrender}} = \frac{9}{8} = 9 : 8 \] Thus, the sacrificing ratio of S and T will be 9 : 8.