A and B invest in the ratio 3 : 5. After 6 months, C joins with the same amount as B. At the end of one year, in what ratio should A : B : C share the profit?

Problem restatementDetermine the profit-sharing ratio when partners invest different amounts and join at different times within a 1-year (12-month) period.

Given data

• Capital ratio initially: A : B = 3x : 5x for 12 months.
• C joins after 6 months with capital equal to B, i.e., 5x for 6 months.

Concept/ApproachProfit share ∝ (capital × time).

Step-by-step calculation A units = 3x × 12 = 36x B units = 5x × 12 = 60x C units = 5x × 6 = 30x Ratio = 36 : 60 : 30 = 6 : 10 : 5

Common pitfalls

• Forgetting that C's capital works only for 6 months.

Final Answer6 : 10 : 5