Question

Daman, Mohit and Paras were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. Daman retires. Mohit and Paras decided to share future profits and losses in the ratio of 5 : 3. The gaining ratio of Mohit and Paras will be:

• A. 21 : 11
• B. 3 : 2
• C. 5 : 3
• D. 1 : 1

Hint:

Gaining ratio = New Share – Old Share. Use LCM to simplify fractional comparisons correctly.

Answer 1

The Correct Option is A

Step 1: Old Ratio (Daman : Mohit : Paras) = 4 : 3 : 2
Total parts = 4 + 3 + 2 = 9
Old share of Mohit = $\dfrac{3}{9}$, Old share of Paras = $\dfrac{2}{9}$

Step 2: New Ratio between Mohit and Paras = 5 : 3
Total parts = 8
New share of Mohit = $\dfrac{5}{8}$, New share of Paras = $\dfrac{3}{8}$

Step 3: Calculate Gaining Share
Gaining Ratio = New Share – Old Share
Mohit’s Gain = $\dfrac{5}{8} - \dfrac{3}{9}$
$\Rightarrow$ $\dfrac{45 - 24}{72} = \dfrac{21}{72}$
Paras’s Gain = $\dfrac{3}{8} - \dfrac{2}{9}$
$\Rightarrow$ $\dfrac{27 - 16}{72} = \dfrac{11}{72}$

Step 4: Gaining Ratio = 21 : 11