VeritasKarishma
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 mL of rum. How much guava juice is in the bottle?
A. 168 mL
B. 170 mL
C. 200 mL
D. 210 mL
E. 250 mL
enigma123: Here is the solution.
We know that the bottle is 80% full. This means that it is 20% empty. This 20% is filled up when you put 70 ml of rum. Since 20% of the bottle is 70 ml, 80% (i.e. 4 times), will be 280 ml (4 times).
So the total volume of the liquid in the bottle is 280 ml. 60% of this 280 ml is guava juice and 40% is pineapple juice.
60% of 280 = 168ml
In % questions, focus on the base i.e. 60% of what? Is it 60% of the bottle or is it 60% of the liquid.
Sharing the step-by-step approach using algebra1. Let the volume of the bottle be \(x\)
2. We are told that the actual contents in the bottle constitute \(80%\) of the bottle i.e. \(\frac{4x}{5}\)
3. Guava constitutes \(60%\) of the contents or \(\frac{4x}{5} * \frac{3}{5} = \frac{12x}{25}\)
4. Pineapple constitutes \(40%\) of the contents or \(\frac{4x}{5} * \frac{2}{5} = \frac{8x}{25}\)
5. The remaining \(20%\) of the bottle is filled with Rum i.e. \(1 - \frac{4x}{5} = 70\)
-> \(\frac{x}{5} = 70\)
-> \(x = 350\)
6. We are asked to find the volume of Guava, which would be \(\frac{12x}{25} = \frac{12 * 350}{25} = 168\)
mlAns.
A