Question

A sample of clay was partially dried. It was then found to contain $50\%$ silica and $7\%$ water. The original clay contained $12\%$ water. Find the percentage of silica in the original sample (as nearest integer).

Answer 1

(a) For partially dried clay

Per cent of silica is 50%, per cent of water is 43%. Hence, percent of silica + water is $50+7=57$ %.

The percent of impurity $=100-57=43$ %

The ratio of weight of silica to weight of impurity $=\frac{50}{43}$.
(b) For original sample,

percent of water is 12%, the percent of silica + impurity $=100-12=88$.

Let x be the percentage of silica.

$\frac{x}{88-x}=\frac{50}{43}$

$x=47$ %

Hence, the percentage of silica in the original sample is 47%.