A begins a business with ₹85,000. Later, B joins with ₹42,500. If year-end profits are shared in the ratio 3 : 1 (A : B), for how many months did B's capital remain invested?

Problem restatementFind B's joining duration given capitals and the final profit ratio over a 12-month year.

Given data

• A: ₹85,000 for 12 months.
• B: ₹42,500 for t months.
• Profit ratio A : B = 3 : 1.

Concept/ApproachProfit share ∝ capital × time.

Step-by-step calculation 85,000 × 12 : 42,500 × t = 3 : 1 10,20,000 : 42,500t = 3 : 1 10,20,000 ÷ (42,500t) = 3 ⇒ 10,20,000 = 1,27,500t t = 10,20,000 ÷ 1,27,500 = 8 months

Final Answer8 months