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Numerical Questions · Q11

Q.Sandeep and Navdeep are partners in a firm sharing profits in 5:3 ratio. They admit C into the firm and the new profit sharing ratio was agreed at 4:2:1. Calculate the sacrificing ratio?

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Sandeep sacrifices 3/56 and Navdeep sacrifices 5/56; Sacrificing Ratio = 3:5.

Concept: Sacrificing Ratio on Admission of a Partner

When a new partner is admitted, the old partners give up (sacrifice) a portion of their profit share in favour of the incoming partner. The sacrificing ratio measures how much each old partner has surrendered. It is calculated as:

Sacrificing Ratio = Old Share - New Share

This ratio determines how the new partner's share of goodwill (if brought in) will be distributed among the old partners—each old partner receives goodwill compensation in proportion to what they sacrificed.

The accounting treatment hinges on understanding that the sacrifice is not simply the difference in absolute fractions but the relative sacrifice between the old partners. We compute each partner's sacrifice, then express those sacrifices as a ratio.


Solution

Step 1: Identify the shares

PartnerOld RatioNew Ratio
Sandeep5/84/7
Navdeep3/82/7
C—1/7

Step 2: Calculate each old partner's sacrifice

To subtract fractions with different denominators, we need a common denominator. The LCM of 8 and 7 is 56.

For Sandeep:

Sacrifice = 5/8 - 4/7 = 35/56 - 32/56 = 3/56

For Navdeep:

Sacrifice = 3/8 - 2/7 = 21/56 - 16/56 = 5/56

Step 3: Express the sacrifices as a ratio

Sandeep's sacrifice : Navdeep's sacrifice = 3/56 : 5/56

Multiply through by 56 to clear denominators:

3 : 5 …

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