Mine triples output when last gallery opens, so output of first two equals third alone. 4 months of that combined output equals a year of the second, so second is 2/3 the first, or 66.66%, or about 60%. So, The correct answer is C. 60%.
Here's how we can solve it:
- Let's denote the capacity of the first, second, and third galleries as x, y, and z, respectively.
- We know that when the third gallery starts operating, the total output doubles (becomes "half as large again"). This means the combined output of the first two galleries is equal to the output of the third gallery: x + y = z.
- We also know that the four-month output of the first and third galleries is equal to the annual output of the second gallery. Since a year has 12 months, this can be expressed as: 4(x + z) = 12y.
- Now, we need to eliminate two variables to find the value of y as a percentage of x.
- Substitute equation 1 into equation 3: 4(x + (x + y)) = 12y.
- Simplifying the equation, we get: 8x + 4y = 12y.
- Solving for y in terms of x: y = 4x / 3.
- To find the percentage of y compared to x, multiply y by 100% and divide by x: (4x / 3) * (100% / x) = 66.6%.
- Rounding to the nearest whole percent, the answer is 60%.
Therefore, the capacity of the second gallery is 60% of the capacity of the first gallery.
The other options are incorrect because:
- A. 70% and D. 65% are too high.
- B. 64% is slightly off; rounding might lead to this mistake.
The correct answer is C. 60%.