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50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4┬аm3, then the rise in the water level in the tank will be:
35 cm
20 cm
50 cm
25 cm
25 cm
Calculate total volume V=50├Ч4=200m3. Then, divide by surface area (40├Ч20=800) to get h=0.25m, which is 25cm.
Number of men = 50, Length of tank = 40 m, Breadth of tank = 20 m, Average water displacement per man = 4 cubic meters.
V=L├ЧB├Чh
Calculate total volume V=50├Ч4=200m3. Then, divide by surface area (40├Ч20=800) to get h=0.25m, which is 25cm.
Confusing meters with centimeters; remember to convert the final result from m to cm by multiplying by 100.
Calculate total volume of displaced water
Since 50 men each displace 4m3 of water, the total volume V raised is 50├Ч4.
V=50├Ч4=200m3
Calculate surface area of the tank
The surface area A of the tank is length multiplied by breadth.
A=40m├Ч20m=800m2
Calculate the rise in water level (h)
The volume displaced is equal to the surface area times the height (h) of the rise, so h=AVтАЛ.
h=800200тАЛ=0.25m
Convert height to centimeters
Convert meters to centimeters by multiplying by 100.
h=0.25├Ч100=25cm
D is correct because the calculated rise in the water level is exactly 25 cm.
This type of volume-to-height problem is standard in fluid dynamics and reservoir management questions in competitive exams.