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Kim and Sim are partners in a firm sharing profits in 4:3 ratio. They admitted Pim as a new partner for 1/4 share in the profits, which he acquired in the ratio of 3:2 from Kim and Sim. Determine the new profit sharing ratio of the partners.

Solution

✅ Correct Option: 4

Given Information:

  • Kim and Sim's old ratio = 4:3
  • Pim admitted for 1/4 share
  • Pim acquires from Kim and Sim in ratio 3:2

Calculating Sacrifices:

Pim's share = 14\frac{1}{4}

This 14\frac{1}{4} is sacrificed by Kim and Sim in 3:2 ratio.

Kim's sacrifice = 35×14=320\frac{3}{5} \times \frac{1}{4} = \frac{3}{20}

Sim's sacrifice = 25×14=220=110\frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}


Calculating New Shares:

Kim's old share = 47\frac{4}{7}

Kim's new share = 47−320=80140−21140=59140\frac{4}{7} - \frac{3}{20} = \frac{80}{140} - \frac{21}{140} = \frac{59}{140}

Sim's old share = 37\frac{3}{7}

Sim's new share = 37−110=3070−770=2370=46140\frac{3}{7} - \frac{1}{10} = \frac{30}{70} - \frac{7}{70} = \frac{23}{70} = \frac{46}{140}

Pim's share = 14=35140\frac{1}{4} = \frac{35}{140}


New Profit Sharing Ratio:

Kim : Sim : Pim = 59140:46140:35140\frac{59}{140} : \frac{46}{140} : \frac{35}{140} = 59:46:35

The correct answer is Option 4.

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