A store has cans of orange, pineapple and mixed fruit juices in the ratio 8 : 9 : 15. The store sells 25 percent of the orange, 33.33 percent of the pineapple and 20 percent of the mixed fruit juice cans. What is the ratio of the remaining cans of orange, pineapple and mixed fruit juices in stock?

Introduction / Context:
This ratio and percentage question is based on stock management in a store. Initially, the store has three types of juice cans in a known ratio. A certain percentage of each type is sold, which reduces the quantities. We are asked to determine the new ratio of the remaining cans on the shelves. This problem tests the ability to work with ratios, percentages and proportional reasoning all together.

Given Data / Assumptions:
- Initial ratio of orange : pineapple : mixed fruit juice cans is 8 : 9 : 15.
- 25 percent of orange cans are sold, so 75 percent remain.
- 33.33 percent (approximately one third) of pineapple cans are sold, so two thirds remain.
- 20 percent of mixed fruit cans are sold, so 80 percent remain.
- We need the ratio of remaining orange, pineapple and mixed fruit cans.

Concept / Approach:
We can treat the original ratio as actual counts by assuming a convenient total unit, say 8 orange cans, 9 pineapple cans and 15 mixed fruit cans. Then we apply the given percentages to find remaining cans of each type. After computing the remaining quantities, we express them as a ratio and simplify to obtain the final ratio in lowest terms. The absolute total is not important; only the relative values matter.

Step-by-Step Solution:
Step 1: Assume initial stock: orange = 8 units, pineapple = 9 units, mixed fruit = 15 units. Step 2: Orange sold = 25 percent of 8 = 0.25 * 8 = 2 units, so remaining orange = 8 minus 2 = 6 units. Step 3: Pineapple sold = 33.33 percent of 9 which is about 1/3 of 9 = 3 units, so remaining pineapple = 9 minus 3 = 6 units. Step 4: Mixed fruit sold = 20 percent of 15 = 0.20 * 15 = 3 units, so remaining mixed fruit = 15 minus 3 = 12 units. Step 5: Remaining stock ratio = 6 : 6 : 12. Step 6: Simplify 6 : 6 : 12 by dividing each term by 6 to get 1 : 1 : 2.

Verification / Alternative check:
Instead of using exact counts, we could directly multiply each original ratio term by the remaining fraction. For orange, remaining fraction is 75 percent or 3/4, so 8 * 3/4 = 6. For pineapple, remaining fraction is about 2/3, so 9 * 2/3 = 6. For mixed fruit, remaining fraction is 80 percent or 4/5, so 15 * 4/5 = 12. These values match the earlier calculation, confirming that the final ratio is correctly simplified to 1 : 1 : 2.

Why Other Options Are Wrong:
6 : 6 : 13 would be correct only if mixed fruit remaining were 13 units, which is not supported by the 20 percent sale of 15. 12 : 15 : 19 and 4 : 9 : 13 do not reflect the percentages of sold stock correctly and would imply inconsistent or incorrect percentage reductions. The only ratio that aligns with the computed remaining quantities of 6, 6 and 12 is 1 : 1 : 2.

Common Pitfalls:
Some students treat percentages as absolute quantities instead of fractions of the current count. Another common mistake is incorrectly approximating 33.33 percent and not recognizing it as one third. Others may forget to simplify the final ratio, leaving it as 6 : 6 : 12 instead of reducing to 1 : 1 : 2. Consistent use of fractional or percentage arithmetic avoids these errors.

Final Answer:
The ratio of remaining cans of orange, pineapple and mixed fruit juices is 1 : 1 : 2.