When length of each side of a cube is increased by 3cm, its volume is increased by 2457cm^3. Find its side. How much will the volume decrease, if length of each side of it is reduced by 20%.

Dear Student,

Let a be the side of cube and V be its volume

V = a³            .................... (1) 

If side is increased by 3 then volume increases by 2457

Therefore, V + 2457 = (a+3)³
a³ + 2457 = a³ + 9a² + 27a + 27               (From (1))
9a² + 27a - 2430 = 0
a² + 3a - 270 = 0
a² + 18a - 15a - 270 = 0
a(a+18) - 15 (a + 18) = 0
(a+18)(a-15) = 0
a = 15
V = 15³ = 3375
Now, if length is reduced by 20% 
Therefore, new length = 15 - 20% of 15 = 15 - 3 = 12 

New volume = 12³ = 1728

Decrease in volume = $\frac{3375-1728}{3375}\times 100$
                               = 48.8 %

Regards