12 litres of water are poured into an aquarium of dimensions 50cm leng

Question

12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)

A. 6 
B. 8 
C. 10 
D. 20 
E. 40

HungNguyen · Answer

we have 1 litre = 1000cm³ (thanks Bunuel)
=>12 litres = 12*1000 = 12000cm³

Let call the height of the water is x 
the breadth and length of the water will equal the aquarium 
The volume of the water:
 50 * 30 * x = 12000cm³
=> x = 12000/(50*30) = 8 cm

Answer is B

Another solution:

Let call the height of the space that doesn't contain water is x

First we must find the volume of the aquarium:
 50 * 30 * 40 = 60000 cm³
The volume of the space that doesn't contain water :
 60000-12000 = 48000 cm³
The height of the space:
 50 * 30 * x = 48000 cm³
 => x = 48000/(50*30) = 32
The height of the water:
 the height of the aquarium - x = 40 -32 = 8cm

Answer is B

Divyadisha · Answer

lXbXh= 12000
h= 12000/50*30= 8 cm

'B' is the answer.

rohit8865 · Answer

Another approach
V1/V2=h1/h2

V1 & h1 are volume and height of container
V2 & h2 are volume and height of water to be filled
60000/12000=40/h2
h2=40/5=8cm
Ans B

longhaul123 · Answer

Sorry can someone please explain the logic behind the concept here because i am not understanding how this 1lt =1000 cm^3 making changes to the answer.

arvind910619 · Answer

Hi to get the height we have to convert liters into cm^3 .
As we know volume is measure in either liters or cm^3 or m^3
So to have LHS=RHS we should have variables in same quantity.

Conversion of liters to cum^3 is 
1 Liters = 1000 Cm^3

Hope it helps

Kinshook · Answer

Let the height be x
50*30*x=12*1000
x=8

IMO B

Posted from my mobile device

MathRevolution · Answer

Volume = 12 litres = 12 * 1000 = 12,000  cm^3

Length= 50cm ; Breadth = 30cm

Water rise :  \frac{12000 }{ {50 * 30}}

=>  \frac{120 }{ 15 }

=> 8

Answer B

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12 litres of water are poured into an aquarium of dimensions 50cm leng

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