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Numerical Questions · Q10

Q.Singh, Gupta and Khan are partners in a firm sharing profits in 3:2:3 ratio. They admitted Jain as a new partner. Singh surrendered 1/3 of his share in favour of Jain, Gupta surrendered 1/4 of his share in favour of Jain and Khan surrendered 1/5 in favour of Jain. Calculate new profit sharing ratio?

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The new profit-sharing ratio among Singh, Gupta, Khan, and Jain is 20 : 15 : 24 : 21.

When a new partner is admitted, the old partners surrender a portion of their own share to the newcomer. The key idea is that the new partner’s share is the sum of the fractions surrendered by each old partner. The old partners’ new shares are their original shares minus what they gave away. The ratio is then expressed in whole numbers.

Let’s break it down step by step.


Step 1: Write the old profit-sharing ratio

Singh : Gupta : Khan = 3 : 2 : 3

Total of the old ratio = 3 + 2 + 3 = 8

So their individual shares are:

  • Singh = 3/8
  • Gupta = 2/8 = 1/4
  • Khan = 3/8

Step 2: Calculate the share surrendered by each old partner

  • Singh surrenders 1/3 of his share:

    Surrendered = (1/3) × (3/8) = 3/24 = 1/8

  • Gupta surrenders 1/4 of his share:

    Surrendered = (1/4) × (2/8) = 2/32 = 1/16

  • Khan surrenders 1/5 of his share:

    Surrendered = (1/5) × (3/8) = 3/40


Step 3: Calculate Jain’s share (total surrendered)

Jain’s share = 1/8 + 1/16 + 3/40

Find LCM of 8, 16, 40 = 80

Convert each:

  • 1/8 = 10/80
  • 1/16 = 5/80
  • 3/40 = 6/80

Jain’s share = (10 + 5 + 6)/80 = 21/80


Step 4: Calculate each old partner’s new share

  • Singh’s new share = Old share – Surrendered

    = 3/8 – 1/8 = 2/8 = 20/80

  • Gupta’s new share = 2/8 – 1/16

    = 4/16 – 1/16 = 3/16 = 15/80

  • Khan’s new share = 3/8 – 3/40

    = 15/40 – 3/40 = 12/40 = 24/80


Step 5: Express all shares with a common denominator …

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