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.