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The value of each of a set of silver coins varies as the square of its diameter if thickness remains constant, and it varies as the thickness if the diameter remains constant. If the diameters of two coins are in the ratio $4:3$ what should the ratio of their thicknesses be if the value of the first is $4$ times that of the second?

1. $16:9$
2. $9:4$
3. $9:16$
4. $4:9$

Let value be denoted by V, diameter by D, thickness by T

V = $D^{2}T$

V1 = 16T1

V2 = 9T2

Here, V1 = 4*V2 => 16*T1  = 36*T2

T1/T2 = 36/16 = 9:4 (Option B)
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