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 determine the sacrificing ratio of S and T, we first establish their initial profit allocations and the portions they relinquish.
1. Initial Allocations:
S's allocation = $\frac{3}{5}$ (derived from 3 + 2 = 5)
T's allocation = $\frac{2}{5}$ 2. Portions Relinquished:
S relinquishes $\frac{1}{4}$ of their allocated share: \[ \text{S's relinquishment} = \frac{1}{4} \times \frac{3}{5} = \frac{3}{20} \]
T relinquishes $\frac{1}{3}$ of their allocated share: \[ \text{T's relinquishment} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} \] 3. Deriving the Sacrificing Ratio: To compute the sacrificing ratio, a common denominator is required. The least common multiple of 20 and 15 is 60.
- S's relinquishment expressed with the common denominator: \[ \frac{3}{20} = \frac{9}{60} \]
- T's relinquishment expressed with the common denominator: \[ \frac{2}{15} = \frac{8}{60} \] 4. Sacrificing Ratio: The sacrificing ratio between S and T is calculated as:
\[ \text{Sacrificing ratio} = \frac{\text{S's relinquishment}}{\text{T's relinquishment}} = \frac{9}{8} = 9 : 8 \] Consequently, the sacrificing ratio of S to T is 9 : 8.