\[ \text{C's share} = \frac{1}{6}, \quad \text{Total goodwill} = \text{Rs }60,000 \] \[ \Rightarrow \text{C's share} = \frac{1}{6} \times 60,000 = \text{Rs }10,000 \]
Gaining ratio (equal gain): A : B = 1 : 1
\[ \text{A’s compensation} = \frac{10,000}{2} = \text{Rs }5,000 \] \[ \text{B’s compensation} = \text{Rs }5,000 \]
\[ \begin{array}{l} \text{A’s Capital A/c} \quad \text{Dr.} \quad \text{Rs }5,000 \\ \text{B’s Capital A/c} \quad \text{Dr.} \quad \text{Rs }5,000 \\ \quad \quad \text{To C’s Capital A/c} \quad \text{Rs }10,000 \end{array} \]
\[ \boxed{\text{A and B compensate Rs 5,000 each to C’s Capital A/c for goodwill.}} \]
Given:
Profit sharing ratio of A, B, C = 3 : 2 : 1
C retires → His share = 1/6
His share is taken equally by A and B → Each gets = 1/12
Step 1: New Ratio Calculation
A's new share = 3/6 + 1/12 = 6/12 + 1/12 = 7/12
B's new share = 2/6 + 1/12 = 4/12 + 1/12 = 5/12
C's share = 1/6 (retiring)
New Ratio of A : B = 7 : 5
Step 2: Gaining Ratio
A's gain = 7/12 - 3/6 = 7/12 - 6/12 = 1/12
B's gain = 5/12 - 2/6 = 5/12 - 4/12 = 1/12
Gaining Ratio = 1 : 1
Step 3: Goodwill Share of C
Goodwill of firm = ₹ 60,000
C's share = ₹ 60,000 × (1/6) = ₹ 10,000
Step 4: Amount to be contributed by A and B
Since gain is equal (1 : 1), each will pay half of C's goodwill:
A's share = ₹ 10,000 × 1/2 = ₹ 5,000
B's share = ₹ 10,000 × 1/2 = ₹ 5,000
Journal Entry (Without Raising Goodwill A/c):
Dr. A’s Capital A/c ₹ 5,000
Dr. B’s Capital A/c ₹ 5,000
To C’s Capital A/c ₹ 10,000
(Being C’s share of goodwill adjusted through capital accounts in gaining ratio)
If \(\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0\), then the value of \(x\) is:
Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[
|\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12
\]
Find the area of the parallelogram.
Find the Derivative \( \frac{dy}{dx} \)
Given:\[ y = \cos(x^2) + \cos(2x) + \cos^2(x^2) + \cos(x^x) \]