#### Answer

We must add 150 ml of distilled water.

#### Work Step by Step

Let X represent the amount of water to be added.
After X is added, we obtain a 10% acid solution.
A 40% acid solution has 60% water in it.
A 10% acid solution has 90% water in it.
We use the following guideline to solve this problem:
Amount of water in original solution + Amount of water to be added = Amount of water in final solution.
60% $\times$ 50 + X = 90% $\times$ (50 + X)
$.6 \times 50 +X = .9 \times (50+X)$
30 + X = 45 + $\frac{9X}{10}$
$\frac{10X}{10}$ - $\frac{9X}{10}$ = 15
$\frac{X}{10}$ = 15
Multiply both sides by 10.
X = 150
We must add 150 ml of distilled water.