Question

500 persons took dip in a rectangular tank which is 80m long and 50 m broad. What is the rise in the level of water in the tank if the average displacement of water by a person is 4 cu. m

Answer 1

Solution :-

let the water level rise by H Meter

Displacement of water = 4m^3

Total Volume Displacement By 500 Men

=> 4 × 500 = 2000m^3

Volume of tank = Volume of water displacement

=> 80 × 40 × H = 2000

=> H = 2000/3200

= > 5/8m

= > 62.5cm

The rise in the level is 62.5cm of water in the tank

=============

@GauravSxena01

Answer 2

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ \bold{\underline\purple{here \: we \: know}} \\ \\ \red{1.} \bold \blue{ \: length \: (l)\: of \: rectangle \: \: tank \: is \: 80 \: m .} \\ \red{2.} \bold \blue{ \: breadth \:( b)\: of \: rectangle \: tank \: is \: 50 \: m.} \\ \red{3.} \bold \blue{ \: displacement \: of \: water \: by \: a \: one \: } \\ \bold \blue{person \: in \: a \: tank \: is \: 4 \: {m}^{3} .} \\ \\ \underline \bold\red{so \: \:displacement \: of \: water \: in \: a \: tank \: by \:} \\ \underline \bold\red{ 500 \: persons } = \blue{500 \times 4 = 2000 \: }\bold\blue{ {m}^{3} \: \: \: \: ..(1)} \\ \\ \underline \bold \purple{let \: height \: of \: rectangular \: tank \: is \: h} \\ \\ \underline\bold\blue{to \: find \: volume \: of \: water \: in \: tank} \\ \\ \underline \bold \red{volume\: of \: rectangular \: tank \: } = \bold \purple{ l\times b\times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{80 \times 50 \times h} \\ \\ \bold \red{v.o.r.t} = \bold \purple{(4000 \times h \: \: ) {m}^{3} \: \: \: ..(2) } \\ \\ \underline\bold\blue{as \: we\: know} \\ \\ \underline\bold\purple{volume \: of \: raised \: water \: in \: rectangular } \\ \underline\bold\purple{tank \: is \: equal \: to \: displacement \: of \: water \: in } \\ \underline\bold\purple{ tank\: by \:500 \: person .} \\ \\ \underline\bold\red{hence} \\ \\ \bold\red{volume \: of \: raised \: water \: in \: rectangular } \\\bold\red{tank \:} = \bold\purple{ displacement \: of \: water \: in } \\ \bold\purple{ tank\: by \:500 \: person .} \\ \\ = > \bold \blue{4000 \times h} = \bold \blue{2000} \\ \\ = > \bold \blue{h} = \bold \blue{ \frac{2000}{4000}} = \bold \blue{ \frac{1}{2} } = \bold \blue{0.5 \: m} \\ \\ \underline \bold\red{Hence \: \purple{0.5 \: m} \: level \: of \: water \: rise \: in \: tank.}$