Three partners share profit in the ratio 5 : 7 : 8 for working periods of 14, 8, and 7 months respectively. What was the ratio of their investments?

Problem restatementGiven profit shares and the months each partner remained invested, back out the ratio of investments.

Concept/ApproachProfit ∝ (investment × time). If I₁, I₂, I₃ are investments and t₁, t₂, t₃ their durations, then: I₁t₁ : I₂t₂ : I₃t₃ = 5 : 7 : 8 Thus, I₁ : I₂ : I₃ = (5/14) : (7/8) : (8/7)

Step-by-step calculation Multiply each by LCM(14, 8, 7) = 56: (5/14)×56 = 20 (7/8)×56 = 49 (8/7)×56 = 64 Investment ratio = 20 : 49 : 64

Common pitfalls

• Inverting time factors (dividing instead of multiplying by months).

Final Answer20 : 49 : 64