Question : Arun, Bhushan and Chetan are partners in a firm sharing profits in 3: 2: 3 ratio. They decide to admit Sehzad as a partner. Arun surrendered 1 / 3 of his share in favour of Sehzad, Bhushan surrendered 1/4 of his share in favour of Sehzad and Chetan surrendered 1/5 of his share in favour of Sehzad. The new profit sharing ratio of partner will be
Option 1: 3: 2: 3: 2
Option 2: 2: 2: 1: 1
Option 3: 2: 1: 2: 1
Option 4: None of the above
Correct Answer: None of the above
Solution : Answer = none of the above (i) Calculation of Surrendered share :
Arun's old share $=\frac{3}{8}$, Arun surrenders $\frac{1}{3}$ of $\frac{3}{8}$ in favour of Sehzad, i. e., $\frac{1}{3} \times \frac{3}{8}=\frac{1}{8}$
Bhushan's old share $=\frac{2}{8}$, Bhushan surrenders $\frac{1}{4}$ of $\frac{2}{8}$ in favour of Sehzad, i. e., $\frac{1}{4} \times \frac{2}{8}=\frac{1}{16}$
Chetan's old share $=\frac{3}{8}$, Chetan surrenders $\frac{1}{5}$ of $\frac{3}{8}$ in favour of Sehzad, i. e., $\frac{1}{5} \times \frac{3}{8}=\frac{3}{40}$
Calculation of New Ratios Arun's new share after surrendenng $\frac{1}{8}$ in favour of Sehzad =$\frac{3}{8}-\frac{1}{8}=\frac{2}{8}$ Bhushan's new share after surrendenng $\frac{1}{16}$ in favour of Sehzad =$\frac{2}{8}-\frac{1}{16}=\frac{4-1}{16}=\frac{3}{16}$ Chetan's new share afler surrendenng $\frac{3}{40}$ in favour of Sehzad =$\frac{3}{8}-\frac{3}{40}=\frac{15-3}{40}=\frac{12}{40}$ Sehzad's share is the total of $\frac{1}{8}$ from Arun, $\frac{1}{16}$ from Bhushan and $\frac{3}{40}$ from Chetan =$\frac{1}{8}+\frac{1}{16}+\frac{3}{40}=\frac{10+5+6}{80}=\frac{21}{80}$ Hence, New Ratio of Arun, Bhushan, Chetan and Sehzad is 2:1:1:1. Hence, the correct option is 4.
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