Q. 13

When water freezes into ice, it increases in volume by 10%. Let’s work out in percentage how much it will decrease in volume if the ice melts into water.

Answer :


Given: The percentage increment in volume when water freezes to ice


=10%


Tip:(i) if y is increased by x% then the new value of y is



(ii)decrement percentage


We will try to approach this problem from backwards i.e. We will assume the volume of water that will result from melting of ice and then use the relation given in question to derive the original volume of ice that was present. After following the above steps we have obtained the volume of ice in terms of volume of water that will result due to melting of ice. Now we will subtract the volume of water from the volume of ice to obtain the decrement in volume. Then following tip(ii) we will get the required answer.


Using the theory stated above,


Let us assume the volume of water that will result due to melting of ice be x volume units.


Now according to the given relation and tip(i)


The volume of ice from which the water results is




Now the decrement in volume due to melting of ice:



Now using tip(ii)


The decrement percentage is:



(Note here the previous value = volume of ice)




=9.09%


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