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A, B and C are partners in a firm sharing profits in the ratio of 3:2:1. D is admitted into the firm for 1/4th share in profits, which he gets 1/8th from B. The total capital of the firm is agreed upon as Rs. 1,20,000 and D is to bring in cash equivalent to 1/4th of this amount as his capital. The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. The capitals of A, B and C after all adjustments, are Rs. 40,000, Rs. 35,000 and Rs. 30,000 respectively. Calculate the new capital of A

Solution

✅ Correct Option: 1

Old ratio: A : B : C = 3/6 : 2/6 : 1/6

D's total share = 1/4

  • Gets 1/8 from B
  • Remaining = 1/4 - 1/8 = 1/8 to be sacrificed by A and C in their old ratio 3:1

A's sacrifice = 3/4 × 1/8 = 3/32

C's sacrifice = 1/4 × 1/8 = 1/32

Converting all to denominator 96:

PartnerOld ShareSacrificeNew Share
A48/969/9639/96
B32/9612/9620/96
C16/963/9613/96
D----24/96

New ratio = 39 : 20 : 13 : 24 (total = 96)


Step 2: Calculate New Capitals

Total capital = Rs. 1,20,000

D's capital = 1/4 × 1,20,000 = Rs. 30,000

Remaining for A, B, C = Rs. 90,000, split in ratio 39:20:13 (total 72 parts)

A=3972×90,000=Rs. 48,750 A = \frac{39}{72} \times 90{,}000 = \textbf{Rs. 48,750}
B=2072×90,000=Rs. 25,000 B = \frac{20}{72} \times 90{,}000 = \textbf{Rs. 25,000}
C=1372×90,000=Rs. 16,250 C = \frac{13}{72} \times 90{,}000 = \textbf{Rs. 16,250}

A's new capital = Rs. 48,750

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