Ratio change after adding items: In a rare coin collection, initially there is one gold coin for every three non-gold coins. After adding 10 more gold coins, the ratio of gold to non-gold becomes 1 : 2. What is the total number of coins in the collection now?

Introduction / Context:
This is a ratio-adjustment problem. We model the initial counts using a common multiplier, apply the change (adding 10 gold coins), and set up the new ratio. Solving for the multiplier yields the exact counts before and after the change.

Given Data / Assumptions:

• Initially gold : non-gold = 1 : 3.
• After adding 10 gold coins, gold : non-gold = 1 : 2.
• No non-gold coins are added or removed.

Concept / Approach:
Let initial gold = k and non-gold = 3k. After adding, gold becomes k + 10 while non-gold remains 3k. Enforce the new ratio (k + 10) : 3k = 1 : 2, solve for k, and then compute the final total as (k + 10) + 3k.

Step-by-Step Solution:

Verification / Alternative check:
Check new ratio: 30 : 60 reduces to 1 : 2, exactly as required.

Why Other Options Are Wrong:
50, 60, 70, 80 do not align with the ratio 1 : 2 after adding 10 gold coins under the initial 1 : 3 structure.

Common Pitfalls:
Accidentally adding 10 to both gold and non-gold, or changing the non-gold count, which is not stated in the problem.

Final Answer:
90