Question:
Fresh sludge has moisture content of \(99\%\) and, after thickening, its moisture content is reduced to \(96\%\). The reduction in volume of sludge is
Fresh sludge has moisture content of \(99\%\) and, after thickening, its moisture content is reduced to \(96\%\). The reduction in volume of sludge is
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During sludge thickening,
\[
\boxed{
V_1S_1=V_2S_2
}
\]
because the quantity of dry solids remains constant.
Updated On: Jul 23, 2026
- \(3\%\)
- \(5\%\)
- \(75\%\)
- \(97\%\)
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The Correct Option is C
Solution and Explanation
Concept:
During sludge thickening, the amount of dry solids remains constant while the moisture content decreases.
Hence,
\[
\boxed{
V_1S_1=V_2S_2
}
\]
where
\[
V=\text{Volume of sludge},
\]
\[
S=\text{Percentage of solids}.
\]
Step 1: Calculate the solids content. Initially, \[ \text{Moisture}=99\% \] Therefore, \[ S_1=100-99=1\% \] After thickening, \[ \text{Moisture}=96\% \] Hence, \[ S_2=100-96=4\% \]
Step 2: Calculate the final volume. Using \[ V_1S_1=V_2S_2, \] \[ V_2 = V_1\left(\frac{1}{4}\right) = 0.25V_1 \] Thus, \[ \text{Reduction in volume} = \left(1-0.25\right)\times100 = 75\%. \] Hence, \[ \boxed{\text{Reduction in sludge volume}=75\%.} \] Therefore, the correct option is \[ \boxed{(C)\;75\%.} \]
Step 1: Calculate the solids content. Initially, \[ \text{Moisture}=99\% \] Therefore, \[ S_1=100-99=1\% \] After thickening, \[ \text{Moisture}=96\% \] Hence, \[ S_2=100-96=4\% \]
Step 2: Calculate the final volume. Using \[ V_1S_1=V_2S_2, \] \[ V_2 = V_1\left(\frac{1}{4}\right) = 0.25V_1 \] Thus, \[ \text{Reduction in volume} = \left(1-0.25\right)\times100 = 75\%. \] Hence, \[ \boxed{\text{Reduction in sludge volume}=75\%.} \] Therefore, the correct option is \[ \boxed{(C)\;75\%.} \]
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