Volume of a body decreased three times and its mass increased for 20% of its original value. Find how much the density of the object increased or decreased?

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Answer 1 · 2018-01-29T18:34:56

Suppose,initial density was #d=m/v# (#m# is the initial mass and #v# is the initial volume)

New density is #d' = (m')/(v')# (#m'# is the final mass and #v'# is the final volume)

Now, #(v-v')/v=1/3 or, v'=(2v)/3# and #m' = (4m)/5#

So, we can write, #d'=(4m)/5*3/(2v) = (6/5) m/v= 6/5 d#

So, #d'-d=(6/5-1)m/v = 1/5 m/v#

So, #(d'-d)/d=1/5#

or, #(d'-d)/d *100 = 1/5 *100 = 20#

So,density is increased by #20%#