A sample of clay was partially dried. It then contained `50%` slica and `7%` water. The original clay contained `12%` water find the percentage of silica in the original sample

Explanation

Let us look at this problem using a tabular format,

It is known that `(x)/(93+x)xx100=12.` This means `x = 12.68` parts. So, total parts become `93+12.68 = 105.68`. Percentage of silica in the original sample of clay will therefore be `(50)/(105.68)xx100=47.31%`.
Alternate Method:
In any case whether the silica sample is dried or not the ratio of silica to the unknown substance shall remain same. In the partially dried clay sample the total parts of silica and unknown substance = 50 and 43 respectively. In the original sample the total parts without water would be 88 as there was `12%` water. So, if the amount of silica = 'x' then the amount of unknown substance = `'88 - x'`. So, we can say that `(x)/(88-x)=(50)/(43) rArr 93x=4400 or x=47.31%`.