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.

Answer 2

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 1/4 of his share and T surrenders 1/3 of his share in favour of U. We need to calculate the sacrificing ratio of S and T.

Step 1: Calculate the amount of share surrendered by S and T.

• S's share = 3/5 of the total share.
• T's share = 2/5 of the total share.

Step 2: Calculate the surrendered share by S:

S surrenders 1/4 of his share. Therefore, the surrendered amount from S is:

S's surrendered share = (1/4) × (3/5) = 3/20

Step 3: Calculate the surrendered share by T:

T surrenders 1/3 of his share. Therefore, the surrendered amount from T is:

T's surrendered share = (1/3) × (2/5) = 2/15

Step 4: Find the sacrificing ratio of S and T.

The sacrificing ratio is the ratio of the shares surrendered by S and T. To find the ratio, we first need to express both surrendered shares with a common denominator.
S's surrendered share = 3/20
T's surrendered share = 2/15 The LCM of 20 and 15 is 60.
So, we convert both fractions to have the denominator 60:S's surrendered share = (3/20) × (3/3) = 9/60
T's surrendered share = (2/15) × (4/4) = 8/60

Therefore, the sacrificing ratio of S and T is:Sacrificing ratio = 9:8

Thus, the correct answer is: (A) 9:8