Solve for initial counts from two “give 5 oranges” scenarios Ramesh and Ganesh have some oranges. If Ramesh gives 5 to Ganesh, Ganesh will have thrice as many as Ramesh. If Ganesh gives 5 to Ramesh instead, they will then have equal numbers. What is the initial ratio Ramesh : Ganesh?

Introduction / Context:
Two hypothetical transfers create two linear conditions on the initial counts. Solving them yields the initial numbers and hence their ratio.

Given Data / Assumptions:

• Let initial counts be R (Ramesh) and G (Ganesh).
• Scenario 1: R gives 5 to G ⇒ (G + 5) = 3(R − 5).
• Scenario 2: G gives 5 to R ⇒ (R + 5) = (G − 5).

Concept / Approach:
Translate each scenario into an equation, then solve the pair for R and G. Finally reduce R:G to simplest form.

Step-by-Step Solution:
From scenario 2: R + 5 = G − 5 ⇒ G = R + 10.Substitute in scenario 1: (R + 10 + 5) = 3(R − 5) ⇒ R + 15 = 3R − 15.30 = 2R ⇒ R = 15; hence G = R + 10 = 25.Initial ratio R:G = 15:25 = 3:5.

Verification / Alternative check:
Check scenario 1: after transfer, R = 10, G = 30 ⇒ G is thrice R. Scenario 2: after transfer, both have 20 ⇒ equal.

Why Other Options Are Wrong:
1:3, 5:7, 7:9, 2:3 do not satisfy both transfer conditions simultaneously.

Common Pitfalls:
Placing the “give 5” on the wrong side; forgetting to update both people's counts in each scenario.

Final Answer:
3 : 5