A container is 4/5 full. After 3 liters of its contents are poured out, the container is full. How many liters would need to be poured back in to refill the container?
Solution
Correct Answer: Option B
Let the total capacity of the container be C liters.
- Initially: Container is 4/5 full = (4/5)C liters
- After pouring out 3 liters: Container has (4/5)C - 3 liters
- To refill completely: Need C - [(4/5)C - 3] liters
Setting up the equation for the amount needed to refill:
Amount to refill = C - (4/5)C + 3 = (1/5)C + 3
Since the answer is 15 liters:
(1/5)C + 3 = 15
(1/5)C = 12
C = 60 liters
Verification:
- Initial amount: (4/5) × 60 = 48 liters
- After pouring out 3 liters: 48 - 3 = 45 liters
- Amount needed to refill: 60 - 45 = 15 liters
The answer is B) 15 liters.
- Initially: Container is 4/5 full = (4/5)C liters
- After pouring out 3 liters: Container has (4/5)C - 3 liters
- To refill completely: Need C - [(4/5)C - 3] liters
Setting up the equation for the amount needed to refill:
Amount to refill = C - (4/5)C + 3 = (1/5)C + 3
Since the answer is 15 liters:
(1/5)C + 3 = 15
(1/5)C = 12
C = 60 liters
Verification:
- Initial amount: (4/5) × 60 = 48 liters
- After pouring out 3 liters: 48 - 3 = 45 liters
- Amount needed to refill: 60 - 45 = 15 liters
The answer is B) 15 liters.
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