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A sample of clay was partially dried. It...

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

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In the partially dried clay the total percentage of silica + water = 57%. The rest of 43% must be some impurity. Therefore the ratio of wts. of silica to impurity = `50/43` . This would be true in the original sample of silica.
The total percentage of silica + impurity in the original sample is 88. If x is the percentage of silica, `x/(88-x)=50/43, x=47.3%`
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