Solution

Understanding Sacrificing Ratio:

Sacrificing Ratio = Old Share - New Share

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

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Step 1: Calculate Old Shares

Old ratio of R and S = 5:3

• R's old share = $\frac{5}{8}$85​
• S's old share = $\frac{3}{8}$83​

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Step 2: Calculate New Shares

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

Total parts = 4 + 2 + 1 = 7

• R's new share = $\frac{4}{7}$74​
• S's new share = $\frac{2}{7}$72​

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Step 3: Calculate Individual Sacrifices

R's Sacrifice:

= Old share - New share

= $\frac{5}{8} - \frac{4}{7}$85​−74​

= $\frac{35}{56} - \frac{32}{56}$5635​−5632​ = $\frac{3}{56}$563​

S's Sacrifice:

= Old share - New share

= $\frac{3}{8} - \frac{2}{7}$83​−72​

= $\frac{21}{56} - \frac{16}{56}$5621​−5616​ = $\frac{5}{56}$565​

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Step 4: Find Sacrificing Ratio

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

= $\frac{3}{56} : \frac{5}{56}$563​:565​

= 3 : 5

Answer: Option 3 (3:5)