Question

Tavish, Umesh and Varun were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. Tavish retired. Umesh and Varun decided to share profits and losses in future in the ratio of 5 : 3. The gaining share of Umesh will be :

• A. (\frac{21}{72}\)
• B. (\frac{11}{72}\)
• C. (\frac{45}{72}\)
• D. (\frac{32}{72}\)

Hint:

Gain = New share - Old share. Always convert to same denominator to subtract fractions.

Answer 1

The Correct Option is B

Old Ratio: Tavish : Umesh : Varun = 4 : 3 : 2
Total old share = 4 + 3 + 2 = 9
Tavish retires. So his 4/9 share will be taken by Umesh and Varun in the gaining ratio. New Ratio = 5 : 3 = Umesh : Varun
Umesh's new share = 5/8; Old share = 3/9 = 8/24
Gain = New share - Old share = 5/8 - 3/9
\[ = \frac{45 - 24}{72} = \frac{21}{72} \] But wait, the question asks specifically for the gaining share of Umesh out of Tavish’s share.
Umesh's gain = \(\frac{5}{8} \times \frac{4}{9} = \frac{20}{72}\), Old share = 3/9 = 24/72
So revised calculation:
New share = 5/8; Old share = 3/9 = 24/72
\[ \text{Gain of Umesh} = \frac{5}{8} - \frac{3}{9} = \frac{45 - 24}{72} = \frac{21}{72} \] Oops! Option (A) is correct. Final Answer: \(\frac{21}{72}\)