Q.D and E are partners sharing profits in the ratio of 3:2. Their capitals, after all other adjustments, stand at ₹60,000 and ₹40,000 respectively. They admit F for a 1/5th share, and F brings in ₹30,000 as his capital. No value of goodwill is mentioned in the question. Calculate the hidden goodwill of the firm and pass the necessary journal entry to adjust it, assuming F's remaining share is carved out of D's and E's shares in their old ratio.

Since goodwill is not stated but F's capital is fixed for a known share, the total value the firm is implicitly being valued at can be worked out, and any excess over the actual combined capital is the hidden goodwill.

Step 1 — Determine the new ratio and sacrificing ratio

F is admitted for 1/5th share; the remaining 4/5th is shared by D and E in their old ratio of 3:2.

D's new share = 3/5 × 4/5 = 12/25; E's new share = 2/5 × 4/5 = 8/25; F's share = 1/5 = 5/25

D's sacrifice = 3/5 − 12/25 = 3/25; E's sacrifice = 2/5 − 8/25 = 2/25 → Sacrificing Ratio D : E = 3 : 2

Step 2 — Compute the implied total capital of the reconstituted firm

F brings in ₹30,000 as capital for a 1/5th share. On this basis, the total capital of the firm, if every partner's capital were in proportion, works out to:

Implied Total Capital = F's Capital ÷ F's Share = ₹30,000 ÷ (1/5) = ₹30,000 × 5 = ₹1,50,000

Step 3 — Compute the actual combined capital of all partners

D's capital (after other adjustments) = ₹60,000

E's capital (after other adjustments) = ₹40,000

F's capital = ₹30,000

Actual Combined Capital = ₹60,000 + ₹40,000 + ₹30,000 = ₹1,30,000

Step 4 — Compute the Hidden Goodwill

Hidden Goodwill = Implied Total Capital − Actual Combined Capital = ₹1,50,000 − ₹1,30,000 = ₹20,000

This ₹20,000 is the goodwill of the firm that was never stated directly but is implied by the value F's capital places on the whole firm. It belongs to D and E, who built it up before F's admission.

Step 5 — Adjust F's share of the hidden goodwill through the capital accounts

F must compensate D and E for the share of this hidden goodwill that F will now enjoy — that is, F's own 1/5th share of the ₹20,000: …

As a cross-check: after this entry, F's capital becomes ₹30,000 − ₹4,000 = ₹26,000, and D's and E's capitals rise to ₹62,400 and ₹41,600 respectively. Total = ₹26,000 + ₹62,400 + ₹41,600 = ₹1,30,000 — unchanged, exactly as expe …

A common error is crediting D and E with the WHOLE ₹20,000 hidden goodwill instead of only F's 1/5th share (₹4,000) — since D and E already own their own share of the goodwill within their own capital balances, only the share F must pay for (F's own share) is transferred through this entry. Another mistake is divi …