Skip to main contentSkip to solution

R and S are partners in a firm sharing profits in the ratio of 5:3. They admitted B as a new partner for 1/7th share in the profit. The new profit sharing ratio will be 4:2:1. The sacrificing ratio of R and S is:

Solution

✅ Correct Option: 3

Solution

Understanding Sacrificing Ratio:

Sacrificing Ratio = Old Share - New Share

This represents how much each existing partner gives up for the new partner.


Step 1: Calculate Old Shares

Old ratio of R and S = 5:3

  • R's old share = 58\frac{5}{8}
  • S's old share = 38\frac{3}{8}

Step 2: Calculate New Shares

New ratio of R:S:B = 4:2:1

Total parts = 4 + 2 + 1 = 7

  • R's new share = 47\frac{4}{7}
  • S's new share = 27\frac{2}{7}

Step 3: Calculate Individual Sacrifices

R's Sacrifice:

= Old share - New share

= 58−47\frac{5}{8} - \frac{4}{7}

= 3556−3256\frac{35}{56} - \frac{32}{56} = 356\frac{3}{56}

S's Sacrifice:

= Old share - New share

= 38−27\frac{3}{8} - \frac{2}{7}

= 2156−1656\frac{21}{56} - \frac{16}{56} = 556\frac{5}{56}


Step 4: Find Sacrificing Ratio

Sacrificing Ratio = R's sacrifice : S's sacrifice

= 356:556\frac{3}{56} : \frac{5}{56}

= 3 : 5

Answer: Option 3 (3:5)

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question