Question

Aditya and Bipin entered into a partnership by investing ₹40,000 and ₹50,000 respectively. After 4 months, Aditya made additional investment equal to \(\frac{1}{4}\)th of his investment and Bipin withdrew \(\frac{1}{5}\)th of his investment. The share of Aditya in the profit of ₹16,200 at the end of the year is:

• A. 8280 Rupees
• B. 8320 Rupees
• C. 8400 Rupees
• D. 8480 Rupees

Hint:

Profit sharing = (Capital × Time) ratio

Answer 1

The Correct Option is C

Step 1: Calculate Aditya's capital × time.
First 4 months: \(40000 \times 4 = 160000\).
Additional investment = \(\frac{1}{4} \times 40000 = 10000\).
Next 8 months: \((40000 + 10000) \times 8 = 50000 \times 8 = 400000\).
Total for Aditya = \(160000 + 400000 = 560000\). Step 2: Calculate Bipin's capital × time.
First 4 months: \(50000 \times 4 = 200000\).
Withdrawal = \(\frac{1}{5} \times 50000 = 10000\).
Next 8 months: \((50000 - 10000) \times 8 = 40000 \times 8 = 320000\).
Total for Bipin = \(200000 + 320000 = 520000\). Step 3: Find profit-sharing ratio.
Ratio = \(560000 : 520000\).
Divide by 10000: \(56 : 52\).
Divide by 4: \(14 : 13\). Step 4: Compute Aditya's share.
Total profit = ₹16200.
Aditya's share = \(\frac{14}{14+13} \times 16200 = \frac{14}{27} \times 16200\).
\(16200 \div 27 = 600\).
\(14 \times 600 = 8400\).