Correct Option
Let G represent the initial number of gold coins and N represent the initial number of non-gold coins.
- The initial ratio of gold coins to non-gold coins is given as 1:3. This establishes the relationship N = 3G.
- Subsequently, 10 more gold coins are added. The number of gold coins becomes G + 10, while the number of non-gold coins remains N.
- The new ratio of gold coins to non-gold coins is stated as 1:2. This can be expressed as (G + 10)/N = 1/2, which simplifies to 2(G + 10) = N.
- Substitute the expression for N from the first condition (N = 3G) into the second equation: 2(G + 10) = 3G.
- Solving this linear equation for G: 2G + 20 = 3G, which yields G = 20.
- Using G = 20, calculate N from the initial ratio: N = 3 * 20 = 60.
- The total number of coins in the collection now is the sum of the new number of gold coins and the non-gold coins: (G + 10) + N = (20 + 10) + 60 = 30 + 60 = 90.
Incorrect Options
Options 2 (80), 3 (60), and 4 (50) are inconsistent with the conditions provided in the problem statement. The calculated total number of coins after the addition of 10 gold coins, derived from the given ratios, is 90.