Question

Beaker A contains 1 liter which is 30 percent oil and the rest is vinegar, thoroughly mixed up. Beaker B contains 2 liters which is 40 percent oil and the rest vinegar, completely mixed up. Half of the contents of B are poured into A, then completely mixed up. How much oil should now be added to A to produce a mixture which is 60 percent oil?

Answer 1

Answer:

1.25 liters of oil

Step-by-step explanation:

Volume in Beaker A = 1 L

Volume of Oil in Beaker A = 1*0.3 = 0.3 L

Volume of Vinegar in Beaker A = 1*0.7 = 0.7 L

Volume in Beaker B = 2 L

Volume of Oil in Beaker B = 2*0.4 = 0.8 L

Volume of Vinegar in Beaker B = 1*0.6 = 1.2 L

If half of the contents of B are poured into A and assuming a homogeneous mixture, the new volumes of oil (Voa) and vinegar (Vva) in beaker A are:

$V_{oa} = 0.3+\frac{0.8}{2} \\V_{oa} = 0.7 \\V_{va} = 0.7+\frac{1.2}{2} \\V_{va} = 1.3$

The amount of oil needed to be added to beaker A in order to produce a mixture which is 60 percent oil (Vomix) is given by:

$0.6*V_{total} = V_{oa} +V_{omix}\\0.6*(V_{va}+V_{oa} +V_{omix}) = V_{oa} +V_{omix}\\0.6*(1.3+0.7+V_{omix})=0.7+V_{omix}\\V_{omix}=\frac{0.5}{0.4} \\V_{omix}=1.25 \ L$

1.25 liters of oil are needed.

Answer 2

There is 1.25 litres of oil that should now be added to A to produce a mixture that is 60 per cent oil.

Given

Beaker A contains 1 litre which is 30 per cent oil and the rest is vinegar, thoroughly mixed up.

Beaker B contains 2 litres which are 40 per cent oil and the rest vinegar, completely mixed up.

Half of the contents of B are poured into A, then completely mixed up.

How much oil is in each container?

Contents in beaker A implies;

15% of oil in 1 litre = 0.15 litre of oil

So that, there are 0.15 litres of oil and 0.85 litres of vinegar in beaker A.

Contents in beaker B implies:

55% of oil in 2 litres = 1.1 litres of oil

So that, thee are 1.1 litres of oil and 0.9 litres of vinegar in beaker B.

Half of the contents of B poured into A implies that beaker A now contains:

0.15 litres + 0.55 litres = 0.7 litres of oil

0.85 litres + 0.45 litres = 1.3 litres of vinegar

Then,

The percentage of oil in A is;

$=\dfrac{0.7}{2} \times 100\\\\= 35$

To increase the percentage of oil to 60%, then:

0.7 litres + 1.25 litres = 1.95 litres of oil

And The new total litres of the content in beaker A = 3.25 litres

$=\dfrac{1.95}{3.25}\times 100\\\\=60 \rm \ percent$

Hence, 1.25 litres of oil should now be added to A to produce a mixture that is 60 per cent oil.

To know more about percentages click the link given below.

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