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GATE 2026 CE (CE2) – Question 28

Water and Waste Water Quality and Treatment · Sludge treatment and disposal, reuse of treated sewage · 1 mark · Multiple choice

One-third of the solid matter in a sludge containing 90 % water is composed of fixed mineral solids with specific gravity 2.5, and two-third is composed of volatile solids with specific gravity 1.0.

Specific gravity of all solids lies between

  1. 1.2 and 1.3
  2. 1.5 and 1.6
  3. 1.7 and 1.8
  4. 2.0 and 2.1

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Show answer and explanation

Correct answer: (A) 1.2 and 1.3

Explanation

The fractions are fractions of the mass of the solids, so the volumes add as $\frac{1}{G_s} = \frac{1/3}{2.5} + \frac{2/3}{1.0} = 0.1333 + 0.6667 = 0.8$. So $G_s = \frac{1}{0.8} = 1.25$, which lies between 1.2 and 1.3. The water content of the sludge is not needed.