Question

Rana, Sana and Kamana are partners, sharing profits in the ratio 4:3:2. Rana retires; Sana and Kamana decided to share profits in the future in the ratio of 5:3. The Gaining Ratio of Sana and Kamana will be -

• A. 21:11
• B. 11:21
• C. 11:22
• D. 12:21

Hint:

To calculate the gaining ratio, subtract old share from new share for each partner and simplify the ratio.

Answer 1

The Correct Option is A

Step 1: Old ratio
Rana : Sana : Kamana = 4:3:2 = total 9 parts. \[ \text{Sana old share} = \frac{3}{9} = \frac{1}{3}, \text{Kamana old share} = \frac{2}{9} \]

Step 2: New ratio after Rana retires
Sana : Kamana = 5:3 = total 8 parts. \[ \text{Sana new share} = \frac{5}{8}, \text{Kamana new share} = \frac{3}{8} \]

Step 3: Calculate Gain
\[ \text{Sana's gain} = \frac{5}{8} - \frac{1}{3} = \frac{15 - 8}{24} = \frac{7}{24} \] \[ \text{Kamana's gain} = \frac{3}{8} - \frac{2}{9} = \frac{27 - 16}{72} = \frac{11}{72} \]

Step 4: Express gains in ratio
Take LCM = 72. \[ \text{Sana's gain} = \frac{7}{24} = \frac{21}{72}, \text{Kamana's gain} = \frac{11}{72} \] So ratio = 21 : 11.

Final Answer: \[ \boxed{\text{Gaining Ratio = 21:11}} \]