The Young's modulus and rigidity modulus of a metal are 40 GPa and 20 GPa respecti- vely. Then the bulk modulus is 

Given,

Youngs modulus = 40GPa

rigidity modulus = $20\mathrm{GPa}$

Young's modulus (Y), shear modulus (G), and bulk modulus (B) are related to one another:

$\mathrm{Y}=\frac{9\mathrm{BG}}{3\mathrm{B}+\mathrm{G}}$

Now substituting the values,

$40=\frac{9\mathrm{B}\times 20}{3\mathrm{B}+20}$

$40(3\mathrm{B}+20)=180\mathrm{B}$

$120\mathrm{B}+800=180\mathrm{B}$

$60\mathrm{B}=800$

$\mathrm{B}=\frac{800}{60}$

$\mathrm{B}=13.33\mathrm{GPa}$

Hence the correct answer is 13.33 GPa.