A, B, and C started a business in partnership by investing ₹29,000, ₹50,000, and ₹65,000, respectively. After 8 months, A invested ₹24,000 more while C withdrew ₹15,000. If the profit earned at the end of the year is ₹1,04,000, find the share of C in the profit.

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Let’s solve it step by step carefully:
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### Step 1: Initial Investments
* A = ₹29,000 * B = ₹50,000 * C = ₹65,000
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### Step 2: Changes after 8 months (out of 12 months)
* A adds ₹24,000 → new investment = 29,000 + 24,000 = ₹53,000 (for last 4 months). * C withdraws ₹15,000 → new investment = 65,000 − 15,000 = ₹50,000 (for last 4 months). * B’s investment remains same throughout (₹50,000 for 12 months).
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### Step 3: Calculate investment × time (capital-months)
#### A’s capital
= (29,000 × 8) + (53,000 × 4) = 2,32,000 + 2,12,000 = **₹4,44,000**
#### B’s capital
= 50,000 × 12 = **₹6,00,000**
#### C’s capital
= (65,000 × 8) + (50,000 × 4) = 5,20,000 + 2,00,000 = **₹7,20,000**
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### Step 4: Ratio of their capitals
A : B : C = 4,44,000 : 6,00,000 : 7,20,000
Divide by 12,000 to simplify → A : B : C = 37 : 50 : 60
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### Step 5: Total ratio parts = 37 + 50 + 60 = 147
C’s share = (60 / 147) × 1,04,000 = ₹42,448 (approx.)
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✅ **C’s share of the profit = ₹42,450 (approx.)**

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