At what depth below the surface of the earth the value of g is the same as that at a height of 64 km?

the value of gravitational acceleration below the surface of earth at a distance r from the center of the earth 

= G *(mass of earth exerting gravitational force*)/distance2

= G ( 4/3 * π*r3)ρ /r2 =  4/3*π*G*r*ρ

4/3*π*G*(R-d)  .....(A)

where G = gravitational constant 

r= distance from the center of the earth 

ρ= density of the earth

d = depth below the surface

R= radius of earth

the value of gravitational acceleration above the surface of earth at a height  h from the center of the earth 

= G ( 4/3 * π*R3)ρ/(R+h)2  ...............(B)

equation A = equation of B for value of acceleration of gravity to be equal

4/3*π*G*(R-d)*ρ  =G ( 4/3 * π*R3)ρ/(R+h)2 

(R-d) (R+h)2=R3

using radius of earth = 6371 km ( assumed not provided in the question )

height h = 64 km 

and solving above equation we get d= depth = 126.09 km 

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