In a Slake Durability Index (SDI) test, a rock sample of 500 g undergoes two standard cycles of wetting and drying. The mass of the sample retained after the test is 400 g. The SDI of the sample, in %, is

Question

The primary purpose of mine ventilation is to:

Answer 1

Instead of computing the retained fraction directly, work out how much mass the sample lost and subtract that from the whole.

The sample started at 500 g and came out at 400 g after two standard wetting and drying cycles, so the mass lost to slaking is:

\[ \Delta m = 500 - 400 = 100 \text{ g} \]

As a fraction of the original mass, this loss is:

\[ \frac{100}{500} \times 100 = 20\% \]

The Slake Durability Index reports the part of the rock that did not slake away, so it is the complement of this loss:

\[ SDI = 100\% - 20\% = 80\% \]

Let's summarize:

The rock lost 100 g out of 500 g, which is 20% of its mass, during the two cycles.
SDI reports what remained, not what was lost, so it equals $100\% - 20\% = 80\%$.
An SDI this high means the rock is durable and breaks down only a little under repeated wetting and drying.

So the SDI of the sample works out to 80%, matching option (D).

Answer 2