A and B invested ₹1,20,000 and ₹1,60,000 respectively. A remained for 10 months and B for 7 months. What is the total profit if B…

Question

A and B invested ₹1,20,000 and ₹1,60,000 respectively. A remained for 10 months and B for 7 months. What is the total profit if B's share is ₹16,800?

1. A. ₹34,800 (Correct answer)
2. B. ₹34,000
3. C. ₹10,000
4. D. ₹10,500

Correct Answer

Option A — ₹34,800

Detailed Solution & Explanation

The correct answer is ₹34,800.

Key Points

• In a partnership with unequal durations, profit divides in the ratio of capital × time:
  • A: 1,20,000 × 10 = 12,00,000
  • B: 1,60,000 × 7 = 11,20,000
• Simplify: 1200 : 1120 = 15 : 14.
• B holds 14 parts and receives ₹16,800, so one part = 16,800 / 14 = ₹1,200.
• Total profit = 29 parts × 1,200 = ₹34,800.
• Always reduce the ratio before dividing — working with 15 : 14 rather than the six-figure products removes most of the arithmetic risk.

Additional Information

• Profit in a partnership divides in the ratio of capital × time, often written as the ratio of "monthly equivalents".
• A simple partnership has equal durations, so capital alone decides; a compound partnership varies the duration, as here.
• If a partner is a working partner, any salary or commission is deducted from the profit before the remainder is divided in the capital-time ratio.

प्रश्न (हिन्दी में)

A और B ने क्रमशः ₹1,20,000 और ₹1,60,000 का निवेश किया। A 10 महीने और B 7 महीने तक रहा। यदि B का हिस्सा ₹16,800 है तो कुल लाभ क्या है?

1. A. ₹34,800
2. B. ₹34,000
3. C. ₹10,000
4. D. ₹10,500