A storage tank contains 80 litres of a fuel blend in which ethanol accounts for 15% of the total volume. How many litres of pure ethanol must be added to the mixture so that the proportion of ethanol increases to 32%?

The correct answer is 20 litres.

Step-by-step explanation:

Step 1: Calculate the initial volume of ethanol in the fuel blend.
The tank currently contains 80 litres of fuel blend with 15% ethanol.
Initial volume of ethanol = 15% of 80 litres

$\text{Initial volume of ethanol}=\frac{15}{100}\times 80=12\text{litres}$

Step 2: Formulate the equation after adding pure ethanol.
Let x be the volume of pure ethanol (in litres) added to the mixture.
When x litres of pure ethanol is added:
- New total volume of ethanol = (12 + x) litres
- New total volume of fuel blend = (80 + x) litres

We are given that the target proportion of ethanol in the new fuel blend must be 32% (or 0.32). Setting up the ratio equation:

$\frac{12+x}{80+x}=\frac{32}{100}$

$\frac{12+x}{80+x}=0.32$

Step 3: Solve for x.
Multiply both sides of the equation by (80 + x):

$12+x=0.32\times (80+x)$

Expand the right-hand side:

$12+x=25.6+0.32x$

Subtract 0.32x and 12 from both sides to collect like terms:

$x-0.32x=25.6-12$

$0.68x=13.6$

Divide both sides by 0.68 to isolate x:

$x=\frac{13.6}{0.68}=20$

Conclusion:
Therefore, 20 litres of pure ethanol must be added to increase the ethanol proportion to 32%.