A starts a business with Rs. 3,500. After 5 months, B joins as a partner. After one year from the start, profits are shared in the ratio 2 : 3 (A : B). What is B's capital contribution?

Problem restatementProfit shares reflect capital × time. A invests for 12 months, B for the last 7 months. The final ratio A : B = 2 : 3. Find B's capital.

Given data

• A's capital = 3,500 for 12 months ⇒ 3,500 × 12
• B joins after 5 months ⇒ time = 7 months with capital = x
• Profit ratio = 2 : 3 (A : B)

Concept/ApproachSet the ratio of capital-months equal to 2 : 3 and solve for x.

Step-by-step calculationA : B = (3,500 × 12) : (x × 7) = 2 : 342,000 : 7x = 2 : 3 ⇒ 42,000 × 3 = 7x × 2126,000 = 14x ⇒ x = 9,000

Verification/AlternativeA's share units = 42,000; B's units with x = 9,000 → 63,000, giving 42,000 : 63,000 = 2 : 3.

Common pitfallsTaking B's time as 12 months (he joined 5 months late).

Final AnswerRs. 9,000